REVIEW 5 major objections 5 minor 76 references
Effects of structure on reasoning in instance-level Self-Discover
T0 review · 5 major / 5 minor · reviewed 2026-08-06 · deepseek-v4-flash
Pith's one-line read Instance-level Self-Discover with free-form natural-language plans consistently outperforms the same pipeline with dynamically generated JSON plans, with relative gains up to 18.90% on MATH.
desk verdict A useful instance-level Self-Discover variant, but the structured-vs-unstructured comparison is confounded by unmatched prompts, so the headline claim is not yet supported. read the letter →
The pith
A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.
The reading
What carries the argument
The load-bearing mechanism is the iSelf-Discover loop: SELECT, ADAPT, and REASON. For each task instance t_i, the model first selects a subset of 39 base reasoning modules, rewrites them to fit the instance, then produces a reasoning plan and executes it to emit a final answer, guided by a fixed prompt at each stage. The decisive point is that the same loop is run twice per instance, once with a planning prompt that asks for a plain-English plan and once with a prompt that asks for a JSON plan, so the intended variable is the plan format. Because both plans are generated per instance, the structured-versus-unstructured comparison is not confounded with granularity; the paper's remaining comparisons hold the style fixed and vary whether the plan is instance-level or task-level, and whether few-shot examples are attached.
What would settle it
A controlled run that keeps the planning prompt text, demonstration, and answer instructions identical and switches only the serialization requirement, free-form text versus JSON, would settle whether the format itself carries the penalty; if the gap disappears or reverses with matched prompts, the paper's central claim is not about structure per se.
Extended reading notes
Core claim
On the paper's own terms, the central claim is that when plan generation is performed per problem instance, representing the plan in unstructured plain English is more accurate than representing it in a dynamically generated JSON structure, and the advantage holds across diverse benchmarks and model families. The evidence table shows that on the 200-example MATH subsample, LLaMA-3.1-405B-Instruct rises from 63.50% with a structured plan to 75.50% with an unstructured plan, a relative gain of 18.90%, while Mistral-Large rises from 67.50% to 76.50%, a relative gain of 13.33%. On BBH and T4D the unstructured variant dominates its structured counterpart for both models at both zero-shot and five-shot guidance, and the zero-shot unstructured configuration beats the five-shot structured configuration in several cases. The authors also claim that instance-level planning is not uniformly superior to task-level Self-Discover: task-level planning retains a large edge on the coherent T4D benchmark, while instance-level planning helps most on the diverse BBH, making plan granularity context-dependent.
Load-bearing premise
The comparison treats the structured and unstructured routes as differing only in whether the plan is JSON or natural language; in fact the two planning prompts shown in Appendix B also differ in wording, in their example plan demonstrations, and in answer-format instructions, so those differences could drive the gap instead of the format itself.
Editorial extensions
If this is right
- Systems that require JSON intermediate reasoning should expect an accuracy tax; routing the internal plan through free text and converting only the final answer to structured form may be cheaper than forcing every reasoning step into a schema.
- Zero-shot free-form planning can beat five-shot structured planning, so for diverse tasks the cost of curating exemplars may not pay off; the paper's numbers show a 5-shot structured variant losing to a 0-shot unstructured one on BBH and T4D for both models.
- Plan granularity should be selected by task coherence: task-level Self-Discover remains strong on homogeneous benchmarks like T4D, while instance-level planning helps on heterogeneous ones like BBH; a run-time selector could decide per query.
- On MATH the style of the plan matters as much as whether a plan exists; the same structured/unstructured split produced double-digit relative improvements in both tested models, so plan representation is a first-order variable for mathematical problem solving.
Reading between the lines
- The structured/unstructured gap might shrink or reverse if the same JSON content were produced with constrained decoding rather than instructed generation, since the model then pays no serialization cost while writing keys; this is a testable extension the paper does not run.
- An adaptive compound system could use the paper's per-task granularity results as a cheap classifier signal: for coherent question families fall back to a task-level plan, for diverse streams generate instance-level plans, and reserve JSON only for the final tool-call payload.
- Because the MATH one-shot example is injected into the task description before planning, part of the structured penalty may come from the model having to copy or reference a JSON skeleton in that context; separating the one-shot demonstration from the planning instruction would localize the mechanism.
Editorial analysis
A structured set of objections, weighed in public.
Referee Report
Summary. The paper introduces iSelf-Discover, an instance-level variant of Self-Discover that generates a reasoning plan for each problem, and compares structured plans (dynamically generated JSON) against unstructured plans (natural language) on BBH, T4D, and MATH using LLaMA-3.1-405B-Instruct and Mistral-Large. It reports that unstructured plans are consistently more accurate, with a relative gain up to 18.90% on MATH, and that the optimal plan granularity (instance-level vs task-level) is context-dependent. The empirical comparison is direct and involves no fitted constants, but the central attribution of the performance gap to JSON versus natural-language format is undermined by confounding prompt differences and by the absence of statistical validation.
Significance. If the central claim were established, it would be practically relevant for compound systems and prompting practice, and the instance-level extension of Self-Discover is a reasonable contribution. The paper has several strengths: the method is formally specified, the T4D replication code and dataset and the MATH subsample are released, and the study asks a focused question about the effect of output structure on reasoning. However, the structured and unstructured arms differ in more than serialization format, no significance tests or multiple seeds are reported, and the MATH baseline is not independently run. As presented, the evidence does not yet support the strong causal conclusion in the abstract.
major comments (5)
- [Appendix B, Figure 4; Eqs. (3)-(6)] The structured and unstructured pipelines differ in more than the serialization format. The planning prompts pPU and pPS have different instructions and different 'Example PLAN Step Demonstration' blocks, the following prompts pFU and pFS impose different task demands (e.g., filling in a JSON object vs simply following a plan), and the final output format differs. The literal prompt strings and example plans are not released. Therefore the 18.90% MATH gain in Table 1 cannot be attributed to JSON versus natural-language structure; it may reflect instruction wording, example quality, or the extra formatting burden. The paper also does not describe how final answers are extracted from the two output formats, so the accuracy measure itself may not be format-neutral.
- [Section 5, Table 1] No confidence intervals, significance tests, or multiple seeds are reported. The BBH margins are small (e.g., LLaMA: 87.27 vs 85.05 for 0-shot; Mistral: 85.57 vs 83.14), and per-task results in Tables 5 and 6 show many tasks where the structured variant performs better. The claim of a 'consistent advantage' is not statistically supported as presented.
- [Section 5.1, Table 1 footnote] The MATH baseline was not run separately; the 63.50 (LLaMA) and 67.50 (Mistral) values are simply duplicated from iSelf-Discover (Struct, 0-shot). Since the original Self-Discover pipeline is not reproduced, these numbers cannot serve as an independent baseline, and the 18.90% relative improvement is a comparison to the authors' own structured variant, not to the original framework.
- [Section 4.1, Appendix A] The T4D replication is not validated against the original T4D dataset, which is not public. The reported large gaps (e.g., baseline 100.00 vs structured 73.23 for LLaMA) could be artifacts of the replication procedure rather than genuine differences in method, so conclusions drawn from T4D should be treated with caution unless the replication is validated or the original data become available.
- [Section 7, Limitations] The Limitations section does not acknowledge the confound identified in Appendix B. It lists generalizability and model scope as limitations, but the fact that pPU/pPS and pFU/pFS differ in instructions, demonstrations, and final-output format is a direct threat to the paper's central claim. A matched-instruction ablation is needed to isolate structure from other prompt differences.
minor comments (5)
- [Figure 1] Figure 1(b) contains a typo: 'realtionships' should be 'relationships'.
- [References] The reference list contains formatting errors, such as the broken author list in the Zhou et al. 2024 entry (e.g., 'Ed H., Denny Zhou') and missing access dates for several online references; please fix these.
- [Table 1] The header 'MATH (1-shot)' is confusing because Appendix E describes a one-shot demonstration for both variants and the main text says no 5-shot runs were performed on MATH; clarify the notation and state the absence of 5-shot MATH runs explicitly.
- [Appendix D.2] The stratified sampling procedure for the MATH subsample does not report a random seed or the exact sampling script; the released subsample helps, but a seed would improve reproducibility of the reported numbers.
- [Figure 4] The 'Example PLAN Step Demonstration' blocks are displayed as empty placeholders; if they are populated, the actual content should be released, and if they are empty, that should be stated explicitly.
Circularity Check
No circularity: the paper is an empirical benchmark comparison whose headline claims are measured outcomes, not consequences of definitions or fitted parameters.
full rationale
The paper's central claim is that unstructured iSelf-Discover plans outperform structured JSON plans, with the headline MATH gain of 18.90% relative. This is an empirical comparison between two separately executed pipelines (Eqs. 3-6), not a derivation in which the output is defined in terms of the input. There are no fitted constants, no parameters calibrated to the target benchmark, and no formal theorem whose assumptions contain the conclusion. The structured and unstructured arms are generated from different prompts, but that is a potential experimental confound, not a circularity: the difference in accuracy is measured, not assumed. The only notable identity in the paper is that the MATH 'SELF-DISCOVER (Baseline)' number is the same as the structured zero-shot iSelf-Discover number, which the paper discloses in the Table 1 footnote: 'This value is the same as the Structured zero-shot iSELF-DISCOVER, and is duplicated here for clarity. No separate experiment was run for the MATH baseline.' This duplication does not drive the central unstructured-versus-structured comparison; the paper explicitly states that on MATH the experiments 'focus exclusively on comparing structured versus unstructured reasoning within our proposed iSELF-DISCOVER.' Self-citations to GitHub and Hugging Face resources are reproducibility artifacts, not load-bearing evidence for the reasoning-format conclusion. The paper also states that the MATH baseline was not separately run, so no independent result is being misrepresented as one. Because no step reduces by construction to its own inputs, the appropriate circularity score is 0.
Assumptions & free parameters
assumptions (4)
- domain assumption The replicated T4D dataset faithfully reproduces the original private T4D benchmark from the ToMi dataset.
- domain assumption The structured and unstructured conditions differ only in output format.
- domain assumption Accuracy on the 200-example MATH subsample is representative of the full MATH test set.
- domain assumption The baseline Self-Discover replication with 10 randomly selected unlabeled examples matches the original method.
Cite this review
Pith. "Pith review of Effects of structure on reasoning in instance-level Self-Discover." pith.science (2026). https://pith.science/paper/QEWRRYOB
@misc{pith2026250703347,
author = {Pith},
title = {Pith review of: Effects of structure on reasoning in instance-level Self-Discover},
year = {2026},
howpublished = {\url{https://pith.science/paper/QEWRRYOB}},
note = {Machine review of arXiv:2507.03347}
}
read the original abstract
The drive for predictable LLM reasoning in their integration with compound systems has popularized structured outputs, yet concerns remain about performance trade-offs compared to unconstrained natural language. At the same time, training on unconstrained Chain of Thought (CoT) traces has brought about a new class of strong reasoning models that nevertheless present novel compute budget and faithfulness challenges. This paper introduces iSelf-Discover, an instance-level adaptation of the Self-Discover framework, and using it compares dynamically generated structured JSON reasoning with its unstructured counterpart. Our empirical evaluation across diverse benchmarks using state-of-the-art open-source models supports a consistent advantage for unstructured reasoning. Notably, on the complex MATH benchmark, unstructured plans achieved relative performance improvements of up to 18.90\% over structured approaches. Zero-shot unstructured iSelf-Discover variants are also shown to outperform their five-shot structured counterparts, underscoring the significance of this gap, even when structured plans are dynamically generated to ensure reasoning precedes the final answer. We further demonstrate that the optimal granularity of plan generation (instance-level vs. task-level) is context-dependent. These findings invite re-evaluation of the reliance on structured formats for complex problem-solving and how compound systems should be organized.
Figures
Figures from the paper (2 more)
Reference graph
Works this paper leans on
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[1]
Identifying characters involved in the story scenario through templated narrative cue words: “entered”, “moved”, and “exited”
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We make our replication publicly available as: 1
Tracking the object of interest and charac- ter who moves the object by the cue word “moved”. We make our replication publicly available as: 1. Code: The python script used to convert the ToMi dataset into T4D. ( https://github. com/sachith-gunasekara/t4d) 2. Dataset: The converted dataset using the above script. ( https://huggingface.co/ datasets/sachith...
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date_understanding: Tests comprehension of dates, including relative dates and date arithmetic
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disambiguation_qa: Requires resolving am- biguities in questions to provide correct an- swers
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9 ADAPT SELECTED module descriptions: 1 How could I devise
dyck_languages: Involves checking the va- lidity of strings based on Dyck language rules (e.g., balanced parentheses). 9 ADAPT SELECTED module descriptions: 1 How could I devise... 2 Make a list of ideas...11 ... Task: Task Description Here are some other examples like the above task: <examples>Example 1 Example 2</examples> Adapt each reasoning module de...
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boolean_expressions: Evaluates the model’s ability to evaluate complex Boolean expressions
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causal_judgement: Assesses understanding of cause-and-effect relationships from textual descriptions
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hyperbaton: Requires understanding sen- tences with inverted or non-standard word or- der (hyperbaton)
Show all 76 references
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logical_deduction_five_objects: Tests deductive reasoning with statements involving five objects
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logical_deduction_seven_objects: Tests deductive reasoning with statements involving seven objects
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formal_fallacies: Tests the ability to iden- tify formal logical fallacies in arguments
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geometric_shapes: Assesses understanding of properties and relationships of geometric shapes
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multistep_arithmetic_two: Involves solv- ing multi-step arithmetic problems, often with two-digit numbers or two operations
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If you take 2 steps forward, then 1 step left, are you at your starting point?
navigate: Requires understanding and fol- lowing navigational instructions (e.g., "If you take 2 steps forward, then 1 step left, are you at your starting point?")
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object_counting: Tests the ability to count objects described in a text
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logical_deduction_three_objects: Tests deductive reasoning with statements involving three objects
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movie_recommendation: Assesses the abil- ity to make movie recommendations based on preferences or descriptions
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ruin_names: Requires identifying "ruined" or slightly altered names
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salient_translation_error_detection: Tests the ability to detect salient errors in machine-translated text
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snarks: Involves understanding and respond- ing to "snarks" – sarcastic or subtly critical remarks, often posed as math or logic prob- lems
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penguins_in_a_table: Involves reasoning about data presented in a tabular format, specifically about penguins
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reasoning_about_colored_objects: Tests reasoning about properties and relationships of colored objects
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tracking_shuffled_objects_five_objects: Tests the ability to track the positions of five objects that are shuffled
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tracking_shuffled_objects_seven_objects: Tests the ability to track the positions of seven objects that are shuffled
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tracking_shuffled_objects_three_objects: Tests the ability to track the positions of three objects that are shuffled
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10 FOLLOW Reasoning Structure: Task: Task Description Correctly follow the above JSON reasoning structure to solvethe given task below
sports_understanding: Assesses compre- hension of sports-related events, rules, and scenarios. 10 FOLLOW Reasoning Structure: Task: Task Description Correctly follow the above JSON reasoning structure to solvethe given task below. Your response should be the filled JSON for th...
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temporal_sequences: Requires understand- ing and reasoning about the order of events in time
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Does the problem involve decision-making or planning, where choices need to be made under uncertainty or with competing objectives?
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Is the problem an analytical one that requires data analysis, modeling, or optimization techniques?
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Is the problem a design challenge that requires creative solutions and innovation?
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web_of_lies: Tests logical deduction to de- termine the truthfulness of individuals based on a set of interconnected statements where each person either tells the truth or lies
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word_sorting: Requires sorting a given list of words into alphabetical order. D Subsampling 200 Examples from the MATH Dataset This section details the methodology used to sub- sample 200 examples from the MATH test dataset for our experiments, along with the statistics of thi...
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Analyzing the distribution of examples across different problem types (e.g., Algebra, Geom- etry) and difficulty levels (Level 1 to Level 5) in the full 5000-example test set
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Performing a stratified sampling to select 200 examples such that the proportions of each problem type and each difficulty level were maintained as closely as possible to the origi- nal distributions. While we followed the precedent set by the SELF -DISCOVER framework (Zhou et...
2024
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level” (e.g., “Level 1
The “level” (e.g., “Level 1”, “Level 2”, etc.) and “type” (e.g., “Algebra”, “Number The- ory”, etc.) of the current test instance are identified
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The training dataset is filtered to find all exam- ples that match the identified level and type
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Struct” refers to structured iSELF -DISCOVER , and “Unstruct
From this filtered subset, one example is randomly selected to serve as the one-shot demonstration for the current test instance. This instance-specific, dynamic selection of a rel- evant one-shot example mirrors the methodology employed by the original SELF -D ISCOVER frame- ...
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How could I devise an experiment to help solve that problem?
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Make a list of ideas for solving this problem, and apply them one by one to the problem to see if any progress can be made
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How could I measure progress on this problem?
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How can I simplify the problem so that it is easier to solve?
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What are the key assumptions underlying this problem?
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What are the potential risks and drawbacks of each solution?
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What are the alternative perspectives or viewpoints on this problem?
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What are the long-term implications of this problem and its solutions?
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How can I break down this problem into smaller, more manageable parts?
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It focuses on logical reasoning, evidence-based decision- making, and identifying potential biases or flaws in thinking
Critical Thinking: This style involves analyzing the problem from different perspectives, questioning assumptions, and evaluating the evidence or information available. It focuses on logical reasoning, evidence-based decision- making, and identifying potential biases or flaws ...
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Explore unconventional solutions, thinking beyond traditional boundaries, and encouraging imagination and originality
Try creative thinking, generate innovative and out-of-the-box ideas to solve the problem. Explore unconventional solutions, thinking beyond traditional boundaries, and encouraging imagination and originality
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Emphasize teamwork, open communication, and leveraging the diverse perspectives and expertise of a group to come up with effective solutions
Seek input and collaboration from others to solve the problem. Emphasize teamwork, open communication, and leveraging the diverse perspectives and expertise of a group to come up with effective solutions
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Focuses on identifying the underlying causes, feedback loops, and interdependencies that influence the problem, and developing holistic solutions that address the system as a whole
Use systems thinking: Consider the problem as part of a larger system and understanding the interconnectedness of various elements. Focuses on identifying the underlying causes, feedback loops, and interdependencies that influence the problem, and developing holistic solutions...
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Emphasize assessing the potential consequences and likelihood of success or failure, and making informed decisions based on a balanced analysis of risks and benefits
Use Risk Analysis: Evaluate potential risks, uncertainties, and tradeoffs associated with different solutions or approaches to a problem. Emphasize assessing the potential consequences and likelihood of success or failure, and making informed decisions based on a balanced anal...
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Examine personal biases, assumptions, and mental models that may influence problem-solving, and being open to learning from past experiences to improve future approaches
Use Reflective Thinking: Step back from the problem, take the time for introspection and self-reflection. Examine personal biases, assumptions, and mental models that may influence problem-solving, and being open to learning from past experiences to improve future approaches
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What is the core issue or problem that needs to be addressed?
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What are the underlying causes or factors contributing to the problem?
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Are there any potential solutions or strategies that have been tried before? If yes, what were the outcomes and lessons learned?
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What are the potential obstacles or challenges that might arise in solving this problem?
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Are there any relevant data or information that can provide insights into the problem? If yes, what data sources are available, and how can they be analyzed?
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Are there any stakeholders or individuals who are directly affected by the problem? What are their perspectives and needs?
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What resources (financial, human, technological, etc.) are needed to tackle the problem effectively?
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How can progress or success in solving the problem be measured or evaluated?
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What indicators or metrics can be used?
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Is the problem a technical or practical one that requires a specific expertise or skill set? Or is it more of a conceptual or theoretical problem?
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Does the problem involve a physical constraint, such as limited resources, infrastructure, or space?
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Is the problem related to human behavior, such as a social, cultural, or psychological issue?
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Does the problem require addressing systemic or structural issues rather than just individual instances?
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Is the problem time-sensitive or urgent, requiring immediate attention and action?
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What kinds of solution typically are produced for this kind of problem specification?
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Given the problem specification and the current best solution, have a guess about other possible solutions
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Let’s imagine the current best solution is totally wrong, what other ways are there to think about the problem specification?
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What is the best way to modify this current best solution, given what you know about these kinds of problem specification?
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Ignoring the current best solution, create an entirely new solution to the problem
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Let’s think step by step
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Figure 5: List of the 39 Base Reasoning Modules
Let’s make a step by step plan and implement it with good notion and explanation. Figure 5: List of the 39 Base Reasoning Modules. 17
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Reviewed August 6, 2026 · model on record in the stance chip above.
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