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REVIEW 3 major objections 5 minor 97 references

By separating per-query reasoning from reusable solver code, SCOPE reports higher multi-constraint planning success with lower cost and latency.

Reviewed by Pith at T0; open to challenge. T0 means a machine referee read the full paper against a public rubric. the ladder, T0–T4 →

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T0 review · deepseek-v4-flash

2026-08-03 10:41 UTC pith:SB2KXECA

load-bearing objection The reusable-solver abstraction is genuinely new and the TravelPlanner results look strong, but the Trip Planning SOTA claim is undercut by mismatched test sets and the latency claim contradicts the paper's own appendix. the 3 major comments →

arxiv 2601.09097 v4 pith:SB2KXECA submitted 2026-01-14 cs.AI

Programming over Thinking: Efficient and Robust Multi-Constraint Planning

Derrick Goh Xin Deik , Quanyu Long , Zhengyuan Liu , Nancy F. Chen , Wenya Wang This is my paper
classification cs.AI
keywords multi-constraint planninglarge language modelsreusable solver functionsstructured representationcode generationplanning efficiencysingle-example learning
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

SCOPE is a planning framework that makes an LLM write reusable code once per problem domain, then answer new queries by filling in parameters rather than re-reasoning in text. From a single example query and answer, LLM agents extract a structured representation — 'combinations' that span the candidate plans and 'constraints' that filter them — and generate three small solver functions that enumerate, filter, and format results. At inference only the per-query parameter values are generated by the model; the solver code is never regenerated. The paper reports that on a travel-planning benchmark this reaches 93.1% success with a current language model, a 61.6-point gain over the strongest text-reasoning baseline, while cutting inference cost by 1.4x and time by about 4.7x, and similar gains on a second natural-language planning benchmark across five models.

Core claim

The paper's central claim is that multi-constraint planning should be decomposed into query-specific reasoning and domain-level execution logic. The framework induces, from one example, a structured representation separating what can vary (combinations) from what must hold (constraints), then builds three reusable functions: one that exhaustively enumerates candidate plans, one that filters them against the constraints, and one that renders the surviving plan as an answer. Since the functions are parameterized only by the structured representation, subsequent queries in the same domain require only a short LLM step to extract their combinations and constraints before the same solver code run

What carries the argument

The load-bearing object is the structured representation: a JSON pair of 'combinations' and 'constraints' plus a matching structured-solution format. It separates the space of candidate plans from the validation logic, which is what lets the solver functions be generic. Three solver functions carry the work: combinations_func() enumerates all candidate plans from the combination parameters, plan_func() filters them against the constraint parameters, and deliver_func() converts the surviving structured plan into natural language. A parameter-free refinement loop compares each function's output against the single example's structured solution and regenerates the function until it matches, whic

Load-bearing premise

Everything rests on a single example query–answer pair being enough to induce solver functions that generalize to every test query in a domain; the paper presents no sensitivity analysis over which example is used.

What would settle it

Seed the same planning domain with several different single example queries and compare the induced solver functions and test success; if swapping the seed changes success materially or any solver function contains hardcoded values from its seed, the one-example-suffices claim is false.

Watch this falsifier — get emailed when new claim-graph text bears on it.

If this is right

  • A planning system built this way pays a small, stable per-query cost (only parameter extraction) after a one-time per-domain solver construction, instead of re-reasoning or regenerating code for every query.
  • Reliability no longer depends on the model's step-by-step consistency at inference time; once the solver functions are validated, candidate enumeration and constraint filtering are deterministic.
  • Weaker, cheaper models become viable for multi-constraint planning because the combinatorial difficulty is absorbed by executable code rather than by model scale.
  • Inference cost and latency scale with the size of the structured inputs, not with the length of the reasoning chain, so hard long-horizon plans remain affordable.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The paper's error analysis locates most failures in the Input Agent, so the next practical gain likely comes from making parameter extraction self-verifying — e.g., checking extracted values against the query — rather than from improving solver generation.
  • The 'one example suffices' claim deserves a sensitivity test: seeding the same domain with different example queries would reveal whether the induced representation generalizes or quietly memorizes example-specific patterns.
  • The exhaustive-enumeration design suggests a tractability boundary: in domains where the combination space explodes, the solver would need sampling or pruning, and the paper's own ablation caps candidate plans at 100,000, hinting that this boundary is real.
  • The underlying recipe — induce a reusable program from a single demonstration, then decode only parameters at inference — likely transfers beyond planning to other structured decision tasks with a shared domain shape, though the paper notes solvers do not yet generalize across domains.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Referee Report

3 major / 5 minor

Summary. The paper introduces SCOPE, a multi-agent LLM framework for multi-constraint planning. The method has two stages: query-specific problem reasoning (problem formalization and optimization) and generic solver generation (construction and refinement of combination, filter, and deliver functions). The resulting solver functions are reusable across queries in the same domain, and inference only requires an Input Agent to convert each query into structured parameters. The authors evaluate SCOPE on TravelPlanner and two Natural Plan tasks (Trip Planning and Meeting Planning) using GPT-4o, GPT-o3, GPT-5, Gemini-1.5-Pro, and Gemini-2.5-Pro, and report large improvements in success rate over Direct, CoT, ToT, EvoAgent, HTP, and ToS, together with claims of lower cost and latency. An ablation study shows that problem formalization, problem optimization, and solver refinement are each important. The code is made publicly available.

Significance. If the empirical claims are supported, SCOPE would be a useful contribution: it offers a concrete mechanism for turning LLM-based reasoning into reusable, executable planning code, and it shows large gains on weaker models. The paper ships code, provides a detailed pipeline, and includes an ablation study; these are positive features. The central idea of separating query-specific parameter extraction from generic solver execution is well motivated and could influence subsequent work on LLM planning. However, the evaluation has at least one load-bearing inconsistency in the Trip Planning comparison, and the headline latency claim needs clarification. The single-example generalization claim also lacks sensitivity analysis. These issues currently prevent the SOTA and efficiency claims from being fully supported.

major comments (3)
  1. [Section 4.1 / Tables 1 and 4] The Trip Planning comparison is not on a clearly common test set. The footnote states that half of the Trip Planning queries were used for some methods, with Direct, CoT, and SCOPE run on the full set and reported in Appendix Table 4. Yet Table 1 reports Trip SR values for Direct/CoT/SCOPE that differ from Table 4 (e.g., GPT-4o Direct: 4.9 vs 4.0; CoT: 3.9 vs 3.4; GPT-o3 CoT: 77.9 vs 77.4). The reader cannot tell whether Table 1's Trip column compares all methods on the same 800 queries or mixes 800-query baseline results with 1,600-query SCOPE results. The claimed SOTA gap (e.g., 87.1% vs 12.5%) is therefore not established. Please either report full-set results for all baselines or restrict Table 1 to the same 800 queries for all methods and move full-set results to Table 4.
  2. [Abstract / Section 5.3 / Table 5] The abstract's headline 'cutting inference cost by 1.4x and time by ~4.67x' is not traceable to the per-query latency table for the cited example. Appendix Table 5 shows GPT-4o TravelPlanner with CoT time 14s and SCOPE time 32s, i.e., SCOPE is about 2.3x slower per query. If the 4.67x claim refers instead to Figure 5's per-correct-solution metric (including repeated failed attempts), say so explicitly and report the corresponding numbers; otherwise the latency claim is contradicted by Table 5. Section 5.3's statement that SCOPE is 'comparable' to CoT on time is also inconsistent with Table 5 for this setting.
  3. [Section 3.3] The claim that 'a single example suffices' is load-bearing for the reusable-solver contribution, but no sensitivity analysis is provided. Solver functions are refined until they reproduce the single example's ground-truth output, and the same example is used as the one-shot inference exemplar. If the chosen example encodes domain-specific patterns (day-overlap conventions, flight-list orientation, output formatting quirks), the induced functions could silently overfit. Please run the pipeline with several different example query–answer pairs and report the variance in test success rates, or provide a formal argument that the refinement procedure cannot encode instance-specific values.
minor comments (5)
  1. [Table 1] There is a typographical error in the GPT-5/ToS row: '36,7' should presumably be '36.7'.
  2. [Section 5.1 and Appendix Table 4] The relationship between Table 1 and Table 4 needs a clear explanatory sentence. As written, the different Trip SR values for Direct/CoT/SCOPE between the two tables are confusing and should be reconciled or explicitly attributed to different query subsets.
  3. [Section 4.3 / Appendix B.4] Several solver-based baselines are excluded with justifications. The exclusions are reasonable, but reporting a single representative ToS baseline may not fully contextualize SCOPE against other code-based methods. A sentence acknowledging this limitation would help.
  4. [General] The paper reports point estimates without variance or repeated runs. Given the large reported gains, reporting standard deviations or confidence intervals for the key comparisons would strengthen the empirical claims.
  5. [Section 1 / Section 3.3] The term 'parameter-free refinement step' is misleading because there are hyperparameters such as refinement patience. Consider rephrasing to 'no learned parameters' or 'no trainable parameters'.

Circularity Check

0 steps flagged

No significant circularity: evaluation is held-out and benchmark-based; the single-example fit is supervised, not self-predictive.

full rationale

Reviewing the claimed derivation chain end to end, I find no step in which a predicted quantity is equal to an input quantity by construction. The method is an empirical pipeline: solver functions are constructed and refined on one example query-answer pair (Section 3.3, Algorithm 1), and final success rates are computed on held-out test queries (Appendix D: 1,000 TravelPlanner, 1,600 Trip Planning, 1,000 Meeting Planning). The refinement loop fits to the single training example only; no test-set answer is used to update functions or prompts. The central performance claims (Tables 1, 4, 5) are external-benchmark measurements and are therefore falsifiable rather than definitional. The only fitting-like component is Solver Refinement, whose target is the same example that produced the structured representations; that is supervised training, not a circular prediction. Concerns that a single example may not generalize are an overfitting/robustness question, not an equation-level identity. The Trip Planning subset mismatch in Table 1 (baselines on 800 queries; SCOPE/Direct/CoT on 1,600) is a serious fairness/validity caveat, but it does not reduce any result to its inputs by construction. The self-citation to Zhang et al. 2025 appears in Related Work and in the exclusion of MTP/PMC; the exclusion is justified via HTP's reported comparison and the argument that SCOPE outperforms HTP, a transitive empirical claim, not a self-referential theorem. It is not load-bearing for the main result.

Axiom & Free-Parameter Ledger

2 free parameters · 4 axioms · 0 invented entities

The central claim is empirical. It rests on assumptions about benchmark formalization, single-example generalization, and the correctness of LLM-generated code. No formal derivation or machine-checked proof is provided.

free parameters (2)
  • refinement patience = 3
    Appendix C.1: 'We set the patience to 3' for regenerating solver functions. No sensitivity analysis is provided, and this cap directly affects whether solver functions converge to the validation example.
  • number of example query-answer pairs = 1
    Section 3.2/3.3: the whole abstraction is induced from a single example per domain. The claim that one example suffices is asserted without example-swap experiments.
axioms (4)
  • domain assumption A solver function that reproduces one example query-answer pair generalizes to unseen queries in the same domain.
    Section 3.3 asserts this without formal proof or sensitivity analysis; it is the core mechanism behind all reported success rates.
  • domain assumption TravelPlanner's commonsense constraints are faithfully represented by the eight deterministic rules in Appendix B.2.
    The closed-environment formalization changes how the benchmark is evaluated; if any rule is wrong or incomplete, the TravelPlanner scores are not directly comparable to official benchmark numbers.
  • ad hoc to paper Parameters that apply uniformly across all candidate plans have no discriminative power and can be removed without changing solutions.
    Optimization Agent prompt in Appendix G uses this heuristic; it removed total_days in the Trip Planning example, relying on other parameters to preserve correctness.
  • domain assumption LLM-generated Python functions are deterministic, executable, and enumerate the full candidate space.
    The framework's reliability argument depends on the generated code being correct and exhaustive; the paper offers only example-based refinement as assurance.

pith-pipeline@v1.3.0-alltime-deepseek · 37420 in / 14620 out tokens · 142721 ms · 2026-08-03T10:41:28.694733+00:00 · methodology

0 comments
read the original abstract

Multi-constraint planning involves identifying, evaluating, and refining candidate plans while satisfying multiple, potentially conflicting constraints. Existing large language model (LLM) approaches face fundamental limitations in this domain. Pure reasoning paradigms, which rely on long natural language chains, are prone to inconsistency, error accumulation, and prohibitive cost as constraints compound. Conversely, LLMs combined with coding- or solver-based strategies lack flexibility: they often generate problem-specific code from scratch or depend on fixed solvers, failing to capture generalizable logic across diverse problems. To address these challenges, we introduce the Scalable COde Planning Engine (SCOPE), a framework that disentangles query-specific reasoning from generic code execution. By separating reasoning from execution, SCOPE produces solver functions that are consistent, deterministic, and reusable across queries while requiring only minimal changes to input parameters. SCOPE achieves state-of-the-art performance while lowering cost and latency. For example, with GPT-4o, it reaches 93.1% success on TravelPlanner, a 61.6% gain over the best baseline (CoT) while cutting inference cost by 1.4x and time by ~4.67x. Code is available at https://github.com/DerrickGXD/SCOPE.

Figures

Figures reproduced from arXiv: 2601.09097 by Derrick Goh Xin Deik, Nancy F. Chen, Quanyu Long, Wenya Wang, Zhengyuan Liu.

Figure 1
Figure 1. Figure 1: The overview workflow of SCOPE. The workflow consists of 2 stages: Query-Specific Problem Reasoning (top-half) and Generic Solver Generation (bottom-half). Different colors of arrows represent different workflow construction: (red, structured representations), (green, structured solution), (gray, solver functions). nation parameters specify elements and properties required to generate candidate plans, wher… view at source ↗
Figure 2
Figure 2. Figure 2: The output of agents at two different stages of [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: The success rate (y-axis) across different level of complexity (x-axis). Top to bottom (Different bench [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: The cost/time required per query (y-axis) for different methods across different level of complexity [PITH_FULL_IMAGE:figures/full_fig_p008_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: The inference cost required per query to reach correct solution. Top to bottom (Different metrics): Number [PITH_FULL_IMAGE:figures/full_fig_p047_5.png] view at source ↗

discussion (0)

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Reference graph

Works this paper leans on

97 extracted references · 2 linked inside Pith

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    GPT-5: gpt-5-2025-08-07

    2025

  2. [2]

    GPT-o3: o3-2025-04-16

    2025

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    GPT-4o: gpt-4o-2024-11-20

    2024

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    Gemini-2.5-Pro: gemini-2.5-pro-preview-05- 06

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    multiple vehicles are booked if capacity is exceeded

    Gemini-1.5-Pro: gemini-1.5-pro-002 B.2 Fairness Considerations To ensure a fair comparison across methods, sev- eral design decisions are enforced. First, few-shot examples are allowed for all methods. For non- solver-based methods such as Direct Prompting, CoT, ToT, and EvoAgent, example queries and their corresponding answers are provided directly in th...

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    If the number of travelers ex- ceeds vehicle capacity, multiple vehicles of the same type are assumed to be booked

    A self-driving car is assumed to have a capac- ity of five people, while a taxi has a capacity of four people. If the number of travelers ex- ceeds vehicle capacity, multiple vehicles of the same type are assumed to be booked

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    Combinations of self-driving with flights or taxis are prohibited

  8. [8]

    Travel between locations occurs on odd- numbered days, while staying within the same city occurs on even-numbered days

  9. [9]

    The same accommodation must be used for two consecutive days within the city

    For each city stay, exactly one accommoda- tion, one attraction, and three distinct restau- rants are required. The same accommodation must be used for two consecutive days within the city

  10. [10]

    If an accommodation’s maximum room capac- ity exceeds the number of travelers, the agent assumes the user will still book the accommo- dation, potentially reserving multiple rooms of the same type

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    If an accommodation requires a minimum number of nights that exceeds the minimum nights specified in the query, the plan is con- sidered invalid

  12. [12]

    Flight costs are computed on a per-ticket ba- sis

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    B.3 Implementation Details of Baselines This section provides a high-level overview of the experimental setup used in evaluating SCOPE and baseline methods

    Restaurants must be unique across the entire trip, repeated restaurant visits are not allowed. B.3 Implementation Details of Baselines This section provides a high-level overview of the experimental setup used in evaluating SCOPE and baseline methods. • Direct Prompting: The model is presented with the query and few-shot demonstrations, and is required to...

    2022

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    Embarcadero to Richmond District:

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    Nob Hill to Financial District: 9

    Nob Hill to Sunset District: 25. Nob Hill to Financial District: 9. Nob Hill to Richmond District: 14. Financial District to Embarcadero:

  16. [19]

    Financial District to The Castro:

  17. [21]

    The Castro to Chinatown: 20

    The Castro to Embarcadero: 22. The Castro to Chinatown: 20. The Castro to Sunset District: 17. The Castro to Nob Hill: 16. The Castro to Financial District: 20. The Castro to Richmond District: 16. Chinatown to Embarcadero: 5. Chinatown to The Castro: 22. Chinatown to Sunset District: 29. 17 Chinatown to Nob Hill: 8. Chinatown to Financial District: 5. Ch...

  18. [22]

    Financial District to Nob Hill: 8

    Financial District to Sunset District: 31. Financial District to Nob Hill: 8. Financial District to Richmond District: 21. Richmond District to Embarcadero: 19. Richmond District to The Castro: 16. Richmond District to Chinatown: 20. Richmond District to Sunset District: 11. Richmond District to Nob Hill: 17. Richmond District to Financial District: 22. C...

  19. [23]

    Financial District to Chinatown:

  20. [24]

    Input Agent - The agent provides set of elements to generate permutations/combinations and constraints as a structured JSON

  21. [25]

    Combination Function Generator Agent - The agent creates a generic function called combinations_func() that takes any set of elements provided by Input Agent to generate the list of possible plans

  22. [26]

    combinations

    Filter Function Generator Agent - The agent creates a generic function called plan_func() that takes in the constraints provided by Input Agent and any list of possible plans outputted by the function created by Combination Function Generator Agent, to generate the most optimal plan that meets the constraints. Based on the few-shot examples queries, you s...

  23. [27]

    combinations

    Input Agent - You instruct the agent on how to identify the set of elements to generate 19 permutations/combinations given a query. You also instruct the agent on how to identify the constraints to tackle such problems. The output format should consist of three keys: "combinations", "constraints" and "solutions", similar to the structured output that you wrote

  24. [28]

    combinations

    Combination Function Generator Agent - The "combinations" from the output of Input Agent will be the combinations_func() input. Hence, based on the output format of "combinations", you instruct the agent on creating a function on how to use the keys to generate possible plans. The function is expected to output list of plans with each plan's format is sim...

  25. [29]

    constraints

    Filter Function Generator Agent - The "constraints" from the output of Input Agent and output of combinations_func() will be the plan_func() input. Based on the output format of "constraints" and "plan", as well as the type of problem, you instruct the agent on creating a function on how to use the keys from "constraints" to filter the plans from "plan". ...

  26. [30]

    combinations

    First, you must analyse the few-shot examples structured solution. For each key in the solution, you must mention what information are essential in point form. All of the information that you listed must be given to "combinations" in your structured output to generate plans that obey the format of structured solution

  27. [31]

    constraints

    Then, you must analyse what are the information that could help filter out all the combination of plans. These information are essential to be given to "constraints" to obtain plan that meet the constraints. Your output format is as below: <start_of_COT> Informations that are essential for generating combinations : <informations in point form> Constraints...

  28. [32]

    Structured output - The agent will provide the combinations and constraints based on the few-shot examples, as well as their 20 corresponding field description

  29. [34]

    combinations

    We define parameter as each key in the "combinations" and "constraints" from structured output. You are required to look at constraints that are not represented in list or JSON

  30. [35]

    We define the parameter with no discriminative power the constraint will either cause all plans to pass or fail

    If the parameter has no discriminative power, the parameter has to be removed. We define the parameter with no discriminative power the constraint will either cause all plans to pass or fail. On the other hand, parameter that can cause one plan to fail and other plan to not fail have discriminative power

  31. [36]

    For example, given the problems produces plan A, B and C, where sum of X for plan A, B and C have the same value, due to plan A,B and C have constant set of items, hence the parameter corresponding to the sum of X should be removed, because it will cause either all plans to pass or fail

  32. [37]

    If the parameter should be removed, you should remove it in the structure output

  33. [38]

    combinations

    Hence, we define the parameter with no discriminative power based on the criteria : The parameter applies uniformly across all of the plans. You MUST consider each key from BOTH "combinations" and "constraints" of the structured output as your parameters. Please ensure your JSON is in correct format and able to be parsed. Do not use "..." to indicate more...

  34. [39]

    <Mention if the parameter has/does not have discriminative power>

    <Parameter Type 1> - <Justify whether the parameter applies/does not apply uniformly across all of the plans>. <Mention if the parameter has/does not have discriminative power>. Hence, it should be <removed/not removed>. ... N. <Parameter Type N> - <Justify whether the parameter applies/does not apply uniformly across all of the plans. <Mention if the par...

  35. [40]

    Structured output - The agent will provide the combinations and constraints based on the few-shot examples, as well as their corresponding field description

  36. [41]

    Combination Function Generator Agent

    Planning instructions - The agent will write instructions to "Combination Function Generator Agent" and "Solution Function Generator Agent". Here is the structured output of Planning Agent: <structured_output> Here is the planning instructions of Planning Agent: <planning> Your main job is as follows:

  37. [42]

    constraints

    You are only required to look at the constraints in the "constraints" of structured output, not "combinations"

  38. [43]

    You must properly check if the same type of constraints exists for every item in the combination space

    Even if the constraint only applies to each item but not all items, you must also see if similar type of constraint applies to other items. You must properly check if the same type of constraints exists for every item in the combination space

  39. [44]

    For example, given the combination space has item A, B and C, and the given type of constraint has 3 constraints, where each constraint is applied to A, B and C, then the same type of constraint exists for every item in the combination space. 21

  40. [45]

    combinations

    If true, then that constraint is a combination parameter, which should be moved to "combinations" in structured output. Please ensure your JSON is in correct format and able to be parsed. Do not use "..." to indicate more items. Your output format is as follows: <start_of_COT>

  41. [46]

    combinations

    <Constraint Type 1> - <Justify whether the type of constraint exists/does not exist in every item in the combination space>. Hence, it is <combination parameters/constraint>. ... N. <Constraint Type N> - <Justify whether the type of constraint exists/does not exist in every item in the combination space>. Hence, it is <combination parameters/constraint>. ...

  42. [47]

    Structured output - The agent will provide the combinations, constraints and structured solution based on the few-shot examples, as well as their corresponding field description

  43. [48]

    Combination Function Generator Agent

    Planning instructions - The agent will write instructions to "Combination Function Generator Agent" and "Solution Function Generator Agent". Here is the list of type of constraints of Planning Agent: <constraints> Here is the structured output of Planning Agent: <structured_output> Here is the planning instructions of Planning Agent: <planning> Your main ...

  44. [49]

    combinations

    We define parameter as each key in the "combinations" and "constraints" from structured output. For each type of parameter, you should check if the type of parameter is expandable. Check if there are any that suggest other parameters should also hold, even if they are not explicitly listed. Rewrite each type of parameters if you think it can be expanded

  45. [50]

    Hence, such parameter can be expanded

    For example, if pair [A,B] exists, then [B,A] might exist, despite not explicitly stated. Hence, such parameter can be expanded. You output Chain-of-Thought to explain your thought process of checking the claim of each parameter and explain whether the parameter is expandable

  46. [51]

    combinations

    You should assume the parameter can be expanded unless there are rules that explicitly stated such expansion cannot be done. You MUST consider each key from BOTH "combinations" and "constraints" of the structured output as the parameter to analyse. Please ensure your JSON is in correct format and able to be parsed. Do not use "..." to indicate more items....

  47. [52]

    solutions

    <Parameter Type 1> - <Justify whether the type of parameter is expandable>. Hence, it is <expandable/non-expandable>. ... N. <Parameter Type N> - <Justify whether the type of parameter is expandable>. Hence, it is <expandable/non-expandablet>. <end_of_COT> <start_of_structured_output> <Your structured output. For the type of parameter that it is expandabl...

  48. [53]

    You mention the difference in pattern in your CoT

    You observe the pattern of ground-truth plan and the pattern of one of the output plan from the list of plans. You mention the difference in pattern in your CoT

  49. [54]

    You should also mention in your CoT that how you should change the CoT thought process of agent to ensure the function generates plan with consistent pattern as the ground-truth plan

  50. [56]

    plan_func()

    Please do not hardcode the function to append the ground-truth plan to the solution. Please do not check the combinations against the ground-truth plan. This defeat the purpose of ensuring the function generates valid plans. Similarly like the original code, the final function should output a list, not a dict. Do not use wrapper like ```python```when writ...

  51. [57]

    You observe the difference between ground-truth plan and the plan that the function returns

  52. [58]

    Check whether is there possibility that each constraint can be handled differently that some plans can meet such constraints

    If the function returns None, it indicates a constraint is handled incorrectly in the code that some plans might meet it but overlooked by the function. Check whether is there possibility that each constraint can be handled differently that some plans can meet such constraints

  53. [59]

    If the function does not return None but returns a different plan than ground-truth, you should reflect whether some constraints are written too lenient that some plans might not meet the constraints but overlooked by the function

  54. [60]

    Once you identified the constraint that is handled incorrectly, you should mention in your CoT that how you should change the CoT thought process of agent to ensure the function handles the constraints correctly

  55. [62]

    deliver_func()

    Please do not hardcode the function to return the ground-truth plan to the solution. This defeat the purpose of ensuring the function returns the correct plan. Similarly like the original code, the final function should output a JSON. Do not use wrapper like```python``` when writing code. Use the wrapper in the provided output format. Your output format i...

  56. [63]

    Does it contain any heading? What does the pattern of output look like?

    You must first analyse the format of few-shot example solution. Does it contain any heading? What does the pattern of output look like?

  57. [64]

    deliver_func()

    Then, you explain how are you going to design the function to ensure the format of your function's output is consistent with the few-shot example solution. Do not miss any heading if the example solution contains 25 heading. Your output format is CoT and Python function as below: <start_of_COT> <your COT> <end_of_COT> <start_of_code> <your deliver_func() ...

  58. [65]

    You mention the difference in pattern in your CoT

    You observe the pattern of ground-truth plan and the pattern of plan that the function returns. You mention the difference in pattern in your CoT

  59. [66]

    You should also mention in your CoT that how you should change the code to ensure the function generates plan with consistent pattern as the ground-truth plan

  60. [67]

    Then, you made the corresponding correction on the agent's code

    You correct the CoT of the agent and write it in your output. Then, you made the corresponding correction on the agent's code

  61. [68]

    next_step

    Please do not hardcode the function to return the ground-truth plan from few-shot examples. Please do not check the output of function against ground-truth plan from few-shot examples. This defeat the purpose of ensuring the function generates plans with valid format. Similarly like the original code, the final function should be a string. Do not use wrap...

  62. [69]

    combinations

    <Condition 1> ... N. <Condition N> Here is an example task called 24 Game and here is the example output description : The 24 Game is a mathematical card game where the objective is to manipulate four integers so that the final result equals 24. The game begins with a list of four numbers, and the player must use each number exactly once, applying any com...

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    The parameter has discriminative power

    cities - The parameter does not apply uniformly across all of the plans as different plans can include different subsets of cities. The parameter has discriminative power. Hence, it should not be removed

  64. [71]

    The parameter does not have discriminative power

    total_days - The parameter applies uniformly across all of the plans as all plans must fit within the total of 21 days. The parameter does not have discriminative power. Hence, it should be removed

  65. [72]

    The parameter has discriminative power

    direct_flights - The parameter does not apply uniformly across all of the plans as different plans can use different direct flights. The parameter has discriminative power. Hence, it should not be removed

  66. [73]

    The parameter has discriminative power

    city_stays - The parameter does not apply uniformly across all of the plans as different plans can have different city stays. The parameter has discriminative power. Hence, it should not be removed

  67. [74]

    combinations

    specific_days - The parameter does not apply uniformly across all of the plans as different plans can meet or not meet specific day requirements. The parameter has discriminative power. Hence, it should not be removed. <end_of_COT> <start_of_structured_output> { "combinations": { "cities": [ "Edinburgh", "Frankfurt", "Dubrovnik", "Vienna", "London", "Buda...

  68. [75]

    This constraint exists for every city in the combination space

    City Stays - The'city_stays' constraint specifies the number of days to stay in each city. This constraint exists for every city in the combination space. Hence, it is a combination parameter

  69. [76]

    combinations

    Specific Days - The'specific_days' constraint specifies exact days for certain cities but not for all cities in the combination space. Hence, it is a constraint. <end_of_COT> <start_of_structured_output> { "combinations": { "cities": [ "Edinburgh", "Frankfurt", "Dubrovnik", "Vienna", "London", "Budapest", "Prague", "Valencia", "Munich", "Oslo" ], "direct_...

  70. [80]

    combinations

    Specific Days - The specific days for visiting certain cities are explicitly defined for events or meetings. There is no indication that additional days should be added. Hence, it is non-expandable. <end_of_COT> <start_of_structured_output> { "combinations": { "cities": [ "Edinburgh", "Frankfurt", "Dubrovnik", "Vienna", "London", "Budapest", "Prague", "Va...

  71. [81]

    **Input Parsing**: We will extract the list of cities, direct flights, and city stays from the input dictionary

  72. [82]

    This will help us in determining valid paths

    **Graph Representation**: We will represent the direct flights as a graph where each city is a node and each direct flight is an edge. This will help us in determining valid paths

  73. [83]

    However, we need to ensure that each sequence is valid in terms of direct flights and total days

    **Permutations and Combinations**: We will use permutations to generate possible sequences of city visits. However, we need to ensure that each sequence is valid in terms of direct flights and total days

  74. [84]

    - We will also calculate the total days required for each sequence by summing up the days required for each city stay

    **Validation of Sequences**: - For each permutation of cities, we will check if there is a direct flight between consecutive cities. - We will also calculate the total days required for each sequence by summing up the days required for each city stay. - If the total days exceed the allowed days, the sequence is invalid

  75. [85]

    The days will be represented as a list of integers

    **Output Format**: For each valid sequence, we will create a list of 38 dictionaries where each dictionary contains the city name and the days spent in that city. The days will be represented as a list of integers

  76. [86]

    city": city,

    **Return the Result**: Finally, we will return a list of all valid sequences in the specified format. By following these steps, we ensure that the function generates all possible valid travel plans according to the given constraints. <end_of_COT> <start_of_code> from itertools import permutations def combinations_func(data): cities = data['cities'] direct...

  77. [87]

    **Input Parsing**: Extract the list of cities, direct flights, and city stays from the input dictionary

  78. [88]

    This will help in determining valid paths

    **Graph Representation**: Represent the direct flights as a graph where each city is a node and each direct flight is an edge. This will help in determining valid paths

  79. [89]

    Ensure that each sequence is valid in terms of direct flights and total days

    **Permutations and Combinations**: Use permutations to generate possible sequences of city visits. Ensure that each sequence is valid in terms of direct flights and total days. 39

  80. [90]

    - Calculate the total days required for each sequence by summing up the days required for each city stay, allowing for overlap between consecutive cities

    **Validation of Sequences**: - For each permutation of cities, check if there is a direct flight between consecutive cities. - Calculate the total days required for each sequence by summing up the days required for each city stay, allowing for overlap between consecutive cities. - If the total days exceed the allowed days, the sequence is invalid

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