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REVIEW 4 major objections 6 minor 7 cited by

Satori: Reinforcement Learning with Chain-of-Action-Thought Enhances LLM Reasoning via Autoregressive Search

T0 review · 4 major / 6 minor · reviewed 2026-08-09 · deepseek-v4-flash

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Pith's one-line read A single 7B LLM can internalize search: 10K Chain-of-Action-Thought demonstrations plus large-scale RL teach it to check steps, correct mistakes, and explore alternatives, yielding top same-scale math benchmark scores.

desk verdict Solid, well-ablated RL recipe for teaching 7B models to self-correct; the SOTA claim hangs on missing baselines and a missing contamination audit. read the letter →

arxiv 2502.02508 v3 pith:A647E6PN submitted 2025-02-04 cs.CL cs.AI

Maohao Shen , Guangtao Zeng , Zhenting Qi , Zhang-Wei Hong , Zhenfang Chen , Wei Lu , Gregory Wornell , Subhro Das
show 2 more authors
David Cox Chuang Gan
This is my paper · ORCID
classification cs.CLcs.AI
keywords chain-of-action-thoughtautoregressivesearchreinforcementlearningself-correctionmathematicalreasoningformattuningrestartandexploretest-timecompute
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

This paper tries to show that the search capability behind test-time scaling can be folded into a single, small language model instead of being split across a generator and an external verifier. Its recipe is a two-stage post-training pass: a small format-tuning stage on 10,000 Chain-of-Action-Thought (COAT) demonstration trajectories, in which each reasoning step is tagged as continuing, reflecting, or exploring, followed by a large reinforcement-learning stage in which the model practices those actions on 300,000 answer-labeled problems. The resulting model, Satori-Qwen-7B, posts higher competition-level math scores than the instruct model built on the same base while using far less supervised data, and it transfers to out-of-domain reasoning tasks. A sympathetic reader would care because it suggests small open models can acquire verifier-like self-checks without hand-labeled reasoning traces or test-time search algorithms.

What carries the argument

The load-bearing object is Chain-of-Action-Thought (COAT) reasoning: a reasoning format whose steps are each tagged with one of three special tokens—continue ($\texttt{<|continue|>}$), reflect ($\texttt{<|reflect|>}$), or explore ($\texttt{<|explore|>}$)—so that ordinary chain-of-thought is the special case that only continues. The argument runs through a two-stage training pipeline: format tuning, which imitates 10K demonstration trajectories synthesized by a generator–critic–reward-model trio and teaches the policy the meaning of the meta-action tokens; and a reinforcement-learning stage using PPO with the Restart-and-Explore (RAE) strategy, where rollouts begin not only from problem statements but also from backtracked partial trajectories of both correct and incorrect solutions, each tagged with a reflect token, creating a diverse initial-state distribution that makes sparse final-answer rewards reachable. The reward combines a rule-based correctness term, a reflection bonus that rewards fixing an incorrect start and penalizes breaking a correct one, and an outcome-reward-model preference score $\sigma(r_\psi)$; between rounds, the current policy is distilled back into the base model before the next RL pass.

What would settle it

Run a contamination check: compute exact and paraphrased overlap between the roughly 550K training questions and the test sets (GSM8K, MATH500, AMC2023, AIME2024, OlympiadBench), then re-evaluate the trained model and the same-base instruct model on freshly generated variants with changed numbers, names, and wording. If the gap shrinks or vanishes, the central claim collapses. Alternatively, add the two concurrent 7B reasoning baselines absent from Table 1 and see whether the reported ordering survives.

Watch

Extended reading notes

Core claim

On its own terms, the paper's discovery is that reinforcement learning can internalize autoregressive search. The authors define Chain-of-Action-Thought reasoning as a token stream in which each step begins with one of three meta-action tokens—continue, reflect, or explore—and then show that a model which has merely imitated 10K COAT demonstrations can be driven by PPO-style reinforcement learning with a restart-and-explore initial-state distribution to a policy that reflects at the right moments and proposes alternative solutions. The behavioral evidence is the shift in self-correction statistics: across in-domain and out-of-domain problems, the trained model's corrections go from mostly harmful (changing right answers to wrong) to mostly helpful, and it generates longer responses on harder problems, allocating more test-time compute where it is needed. On the measured benchmarks the model averages 62.6 percent across GSM8K, MATH500, OlympiadBench, AMC2023, and AIME2024—rising to 64.4 after a second round of self-improvement—against 59.9 for the same-base instruct model, the highest average among the small-scale baselines listed.

Load-bearing premise

The load-bearing premise is that the open-source training corpora—two public math instruction sets plus a consistency-filtered 550K subset—contain no leaked solutions from the evaluation benchmarks, so the reported accuracy gains reflect learned search rather than memorization, and that the state-of-the-art comparison still holds once the concurrent same-scale reasoning baselines missing from the tables are included.

Editorial extensions

If this is right

  • A single 7B model, with no external verifier at inference time, can reproduce much of the benefit that test-time scaling systems obtain by sampling many solutions and scoring them with a separate model.
  • Only 10K demonstration trajectories are needed to make the reasoning format learnable; the remaining gains come from answer-labeled reinforcement learning, cutting reliance on expensive expert reasoning traces.
  • Search behavior is teachable by distillation: weaker base models trained on 240K trajectories generated by the trained model outperform the same bases trained with the original format-tuning pipeline.
  • The pipeline supports continued gains across rounds—the second round raises the math average from 62.6 to 64.4—so it behaves as a self-improvement loop rather than a one-shot fine-tune.
  • Trained on mathematics only, the model still improves on logic, code, commonsense, and tabular reasoning benchmarks, suggesting the reflection-and-explore behavior itself transfers.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • The format-tuning stage may work as a curriculum that converts the sparse final-answer reward into a usable signal by pre-learning the action vocabulary; a testable extension is synthesizing demonstrations with a single self-critiquing model and checking whether RL still converges.
  • Because the learned policy allocates more tokens to harder problems, it has effectively learned a difficulty-conditional compute policy; a testable extension is sampling its COAT rollouts at multiple temperatures and selecting by self-reported confidence, to see whether self-consistency-style gains appear without any voter.
  • If contamination were ruled out, the out-of-domain transfer would suggest that the meta-action structure generalizes rather than the math content; a direct test is retraining the identical recipe on code or logic problem corpora and measuring whether reflect-and-explore behavior transfers back to mathematics.
  • The reflection bonus is asymmetric by design—reward for repairing a wrong start, penalty for breaking a right one; ablating the bonus and the penalty separately would isolate which signal teaches the model when not to reflect.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

4 major / 6 minor

Summary. The paper introduces Chain-of-Action-Thought (COAT), a reasoning format with three meta-action tokens (continue, reflect, explore), and a two-stage post-training recipe for a 7B model: a small-scale format-tuning stage on 10K synthesized COAT trajectories, followed by a large-scale PPO stage with a Restart-and-Explore (RAE) strategy, a reflection bonus, and an outcome-reward-model preference signal. The resulting Satori-Qwen-7B is evaluated on five math benchmarks and six out-of-domain reasoning benchmarks, with additional ablations for COAT versus CoT, RAE, reflection bonuses, ORM rewards, large-scale FT versus RL, and distillation to weaker base models. The paper claims state-of-the-art performance among small models and argues that RL causes the model to internalize autoregressive search, evidenced by improved self-correction statistics and test-time length scaling. Code, data, and models are released.

Significance. If the central empirical claims hold, the paper offers a valuable and unusually transparent post-training recipe: a single 7B model can acquire verify-reflect-explore behavior without an external verifier at inference, using modest human supervision and large-scale RL. The study's strengths include the matched-data COAT-versus-CoT ablation in Table 3, component ablations for RAE, reflection bonus, and ORM rewards in Appendix E, the round-2 distillation result, and the commitment to open-sourcing code, data, and models. The significance is currently conditional on two things: the evaluation benchmarks must be free of overlap with the training corpora, and the 'state-of-the-art' claim must be checked against the concurrent 7B reasoning models the paper itself cites.

major comments (4)
  1. [Section 5 (Benchmark and Evaluation); Appendix D.1]
  2. [Table 1; Section 2 (Concurrent Work)]
  3. [Tables 1, 3, 7, and 8]
  4. [Section 6, Table 4]
minor comments (6)
  1. [Abstract]
  2. [Appendix C]
  3. [Algorithm 1 and Section 4.2]
  4. [Table 4]
  5. [Appendix D.1]
  6. [Section 5.1 and Figure 2]

Circularity Check

0 steps flagged · score 2.0 of 10

No material circularity: central claims rest on independent benchmark evaluation; the one self-citation (rStar filtering) is not load-bearing, and reward-shaped self-correction is an analysis, not a fitted prediction.

full rationale

The paper's central claim is empirical: a 7B model trained with COAT format tuning followed by large-scale RL improves on math benchmarks and transfers out of domain. That claim is grounded in held-out test accuracy (Tables 1 and 2), not in a derived identity. The COAT meta-action tokens are a new proposal rather than an ansatz imported from prior work, and the RL reward is rule-based on ground-truth answers plus an ORM and reflection bonuses whose definitions do not encode the evaluation benchmarks. The one author self-citation is to rStar for mutual-consistency data filtering in Appendix D.1; this is a data-cleaning heuristic, and the paper's central reasoning-ability claims do not depend on that citation being true, so it is not load-bearing. The reflection bonus does directly reward solving from incorrect restart states, which is related to the F-to-T self-correction metric in Table 4, but Table 4 is presented as a behavioral analysis of a trained policy, not as a prediction derived from the training objective, and the headline SOTA claims are benchmark-based. A missing contamination audit of OpenMathInstruct-2/NuminaMath-CoT against AMC/AIME/OlympiadBench would be a correctness risk if test problems leaked into training, but that is not circularity: it concerns whether benchmark gains reflect memorization, not whether a fitted quantity is being relabeled as a prediction. Overall, the derivation chain is self-contained and empirically evaluated, with no step that reduces by construction to its own inputs.

Assumptions & free parameters 4 free parameters · 5 assumptions · 0 invented entities

No new physical or conceptual entity is postulated: the COAT meta-action tokens are vocabulary additions embedded in an explicit training procedure, not unexplained mediators. The load-bearing assumptions are standard RL convergence, answer-format validity, demonstration quality, and benchmark cleanliness. The free parameters are training hyperparameters chosen by the authors, of which the reflection bonus scale is the most visible because it was tuned on the same benchmarks used for the headline results.

free parameters (4)
  • Reflection bonus scale beta = 0.5
    Chosen via ablation on the same benchmark suite used in the headline tables (Appendix E.1, Table 6); no held-out validation is reported.
  • ORM target reward margin tau = 2
    Set in Appendix D.3 without an ablation; affects preference reward quality and therefore RL behavior.
  • Max backtrack steps T in RAE = 2
    Chosen as a hyperparameter in Algorithm 1 and Appendix D.3; controls the restart state distribution.
  • Data budgets (10K FT / 300K RL / 180K round-2 distill) = 10K, 300K, 180K
    Selected by the authors to balance cost and performance; the paper argues small FT plus large RL is better than large FT, but the exact budgets are tuned choices.
assumptions (5)
  • standard math PPO with KL coefficient 0.0 and the stated rollout settings converges to a policy that reflects the intended reward landscape.
    The RL training relies on standard policy-gradient assumptions; Section 4.2 and Appendix D.3 specify PPO without formal convergence guarantees.
  • domain assumption Final-answer string equality is a valid correctness signal for all training and ORM labeling.
    Used in the rule-based reward and in constructing preference pairs (Sections 4.2 and D.3); equivalent mathematical answers with different formatting would be mislabeled.
  • domain assumption The 10K multi-agent demonstration trajectories are diverse and high-quality enough to teach the COAT meta-actions without capping the policy at the generator's ability.
    Format tuning relies on Qwen-2.5-Math-Instruct as generator and Llama-3.1-70B-Instruct as critic (Sections 4.1 and C). If these teachers systematically miss error patterns, the model cannot learn them in FT.
  • domain assumption Training corpora (OpenMathInstruct-2, NuminaMath-CoT, and the QwQ-filtered set) do not overlap with the evaluation test sets.
    No contamination analysis is reported in Appendix D.1; the benchmark claims assume the test questions were not seen during training.
  • ad hoc to paper The QwQ relabeling and mutual-consistency filter preserves the difficulty distribution of the original 550K training set.
    Appendix D.1 uses QwQ to relabel and removes inconsistent answers; if QwQ preferentially succeeds on easier or standard problems, the filtered set may be easier than the raw data.

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Cite this review

Pith. "Pith review of Satori: Reinforcement Learning with Chain-of-Action-Thought Enhances LLM Reasoning via Autoregressive Search." pith.science (2026). https://pith.science/paper/A647E6PN

@misc{pith2026250202508,
  author       = {Pith},
  title        = {Pith review of: Satori: Reinforcement Learning with Chain-of-Action-Thought Enhances LLM Reasoning via Autoregressive Search},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/A647E6PN}},
  note         = {Machine review of arXiv:2502.02508}
}
read the original abstract

Large language models (LLMs) have demonstrated remarkable reasoning capabilities across diverse domains. Recent studies have shown that increasing test-time computation enhances LLMs' reasoning capabilities. This typically involves extensive sampling at inference time guided by an external LLM verifier, resulting in a two-player system. Despite external guidance, the effectiveness of this system demonstrates the potential of a single LLM to tackle complex tasks. Thus, we pose a new research problem: Can we internalize the searching capabilities to fundamentally enhance the reasoning abilities of a single LLM? This work explores an orthogonal direction focusing on post-training LLMs for autoregressive searching (i.e., an extended reasoning process with self-reflection and self-exploration of new strategies). To achieve this, we propose the Chain-of-Action-Thought (COAT) reasoning and a two-stage training paradigm: 1) a small-scale format tuning stage to internalize the COAT reasoning format and 2) a large-scale self-improvement stage leveraging reinforcement learning. Our approach results in Satori, a 7B LLM trained on open-source models and data. Extensive empirical evaluations demonstrate that Satori achieves state-of-the-art performance on mathematical reasoning benchmarks while exhibits strong generalization to out-of-domain tasks. Code, data, and models are fully open-sourced.

Figures

Figures reproduced from arXiv: 2502.02508 by the authors.

Figure 1
Figure 1. A High-level Overview of Satori Training Framework: Format Tuning (FT) + Self-improvement. First, Satori learns COAT reasoning format through imitation learning on small-scale demonstration trajectories. Next, Satori further leverages COAT reasoning format to self-improve via large-scale reinforcement learning. imize the expected cumulative rewards through interactions with an environment. Here, the language model π… view at source ↗
Figure 2
Figure 2. Number of Training Samples of Satori-Qwen-7B and Qwen-2.5-Math-7B-Instruct. Satori-Qwen-7B requires sig￾nificantly less supervision (small-scale FT) and relies more on self-improvement (large-scale RL). For an initial state z ∈ Drestart and a sampled trajectory y˜, the overall reward function r(z, y˜) is defined as: r(z, y˜) = rrule(y˜L, y ∗ ) + σ [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. Policy Training Acc. & Response length v.s. RL Train￾time Compute. Through RL training, Satori learns to improve its reasoning performance through longer thinking. 500 1000 Resp. Len. (# tokens) +269 +305 +330 +362 +394 Level1 Level2 Level3 Level4 Level5 60 80 100 Accuracy (%) +0.7 +2.9 +4.2 +5.8 +6.8 Satori-Qwen Satori-Qwen-FT [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗
Figures from the paper (13 more)
Figure 5
Figure 5. Figure 5: Format Tuning v.s. Distillation. Distilling from a Stronger model (Satori-Qwen-7B) to weaker base models (Llama￾8B and Granite-8B) are more effective than directly applying for￾mat tuning on weaker base models. (300K). Additionally, the large-scale FT model performs si…
Figure 6
Figure 6. Figure 6: Math Domain Example. Satori verifies the correctness of the intermediate steps and proceeds to the next reasoning step. 15 [PITH_FULL_IMAGE:figures/full_fig_p015_6.png]
Figure 7
Figure 7. Figure 7: Math Domain Example. Satori identifies the mistakes in the previous solution and proposes an alternative correct solution. 16 [PITH_FULL_IMAGE:figures/full_fig_p016_7.png]
Figure 8
Figure 8. Figure 8: Math Domain Example. Satori verifies the correctness of previous solution and initiates a different solution. Mathematical Reasoning (from MATH) Problem: Given ∥v∥= 5 and ∥w∥= 8, find the largest possible value of ∥projw v∥. Satori’s Response: The formula for the proje…
Figure 9
Figure 9. Figure 9: Math Domain Example. Satori verifies the correctness of previous solution and further explores a simpler solution. 17 [PITH_FULL_IMAGE:figures/full_fig_p017_9.png]
Figure 10
Figure 10. Figure 10: Math Domain Example. 1) Satori verifies the correctness of intermediate steps in early stage. 2) Satori realizes that the pervious solution is actually erroneous and then proposes an alternative correct solution. 18 [PITH_FULL_IMAGE:figures/full_fig_p018_10.png]
Figure 11
Figure 11. Figure 11: Out-of-domain Example. 1) Satori identifies the potential mistakes in intermediate steps and initiates another solution. 2) Satori realizes that the pervious solution is still erroneous and then proposes an alternative correct solution. Commonsense Reasoning (from Str…
Figure 12
Figure 12. Figure 12: Out-of-domain Example. Satori identifies the potential mistakes in intermediate steps and initiates another correct solution. 19 [PITH_FULL_IMAGE:figures/full_fig_p019_12.png]
Figure 13
Figure 13. Figure 13: Out-of-domain Example. 1) Satori verifies the correctness of intermediate steps in early stage. 2) Satori realizes that the pervious solution is actually erroneous and then proposes an alternative correct solution. 20 [PITH_FULL_IMAGE:figures/full_fig_p020_13.png]
Figure 14
Figure 14. Figure 14: Out-of-domain Example. Satori engages in multiple self-reflection processes during intermediate reasoning steps. 21 [PITH_FULL_IMAGE:figures/full_fig_p021_14.png]
Figure 15
Figure 15. Figure 15: Out-of-domain Example. 1) Satori verifies the correctness of intermediate steps in early stage. 2) Satori realizes that the pervious solution is actually erroneous and then proposes an alternative correct solution. 22 [PITH_FULL_IMAGE:figures/full_fig_p022_15.png]
Figure 16
Figure 16. Figure 16: Out-of-domain Example. Satori identifies the mistakes in previous solution and proposes an alternative correct solution. 23 [PITH_FULL_IMAGE:figures/full_fig_p023_16.png]
Figure 17
Figure 17. Figure 17: Demonstration Trajectories Synthesis. First, multiple initial reasoning trajectories are sampled from the generator and sent to critic to ask for feedback. The critic model identifies the mistake for trajectories with incorrect final answers and proposes an alternativ…

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Forward citations

Cited by 7 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Rethinking Reasoning Quality in Large Language Models through Enhanced Chain-of-Thought via RL

    cs.AI 2025-09 conditional novelty 6.0 of 10

    DRER rewards CoT trajectories that increase the model's likelihood of the correct answer, plus a length penalty, and the new LogicTree benchmark reportedly lifts a 7B model's average accuracy from 0.13 to 0.60.

  2. AdapThink: Adaptive Thinking Preferences for Reasoning Language Model

    cs.LG 2025-06 conditional novelty 6.0 of 10

    AdapThink is an RL post-training framework that adaptively reduces overthinking and underthinking in reasoning language models by rewarding confidence-appropriate reasoning depth and diverse training samples.

  3. Satori-SWE: Evolutionary Test-Time Scaling for Sample-Efficient Software Engineering

    cs.CL 2025-05 conditional novelty 6.0 of 10

    A 32B model trained to self-evolve patch candidates through RL reaches 41.6% on SWE-Bench Verified with 50 samples, comparable to a 70B model using 500 samples.

  4. Pushing Forward Pareto Frontiers of Proactive Agents with Behavioral Agentic Optimization

    cs.AI 2026-02 conditional novelty 5.0 of 10

    BAO, a behavior-enhanced SFT plus regularized RL pipeline, improves proactive agents' task performance while lowering user-involvement rate, beating UserRL baselines on three UserRL gym tasks.

  5. Divide-Fuse-Conquer: Eliciting "Aha Moments" in Multi-Scenario Games

    cs.LG 2025-05 reject novelty 5.0 of 10

    A group, fuse, and retrain recipe for multi-game reinforcement learning lets a 32B model reach near-Claude3.5 performance on several TextArena games, though the headline score is internally inconsistent.

  6. Can 1B LLM Surpass 405B LLM? Rethinking Compute-Optimal Test-Time Scaling

    cs.CL 2025-02 reject novelty 4.0 of 10

    Small LLMs with compute-optimal test-time scaling can outperform much larger models on math benchmarks, but the reported strategy is selected on the same test sets used for evaluation.

  7. A Survey on Large Language Models for Mathematical Reasoning

    cs.AI 2025-06 conditional novelty 1.0 of 10

    Recent advances in LLM mathematical reasoning are organized into comprehension and generation phases, covering methods from prompting to test-time scaling.

Reference graph

Works this paper leans on

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    Seal’s Football and Box: - The seal has a football with a radius of 22 inches. - The dimensions of the box are 52.3 x 43.6 x 36.1 inches. - The volume of the football is given by V = 4 3πr3. V = 4 3π(22)3 ≈ 4 3π(10648) ≈ 44922.67 cubic inches - The volume of the box is: Vbox =...

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    - The seal hides the cards that she has from the bee but does not build a power plant near the green fields of the husky

    Conclusion Based on Rules: - From Rule4: If you see that something hides the cards that she has from the bee but does not build a power plant near the green fields of the husky, what can you certainly conclude? You can conclude that it does not bring an oil tank for the pelika...

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    Therefore, the final answer is: True

    Final Conclusion: - Based on the analysis of the rules and the given information, the seal will bring an oil tank for the pelikan. Therefore, the final answer is: True . Wait. The mistake is that the solution starts analyzing the given information and rules without directly ad...

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    Christopher Reeve suffered a serious spinal cord injury that left him a quadriplegic

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    Christopher Reeve required a portable ventilator after his injury

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    Based on the facts above, answer the following question

    At one point, Christopher Reeve’s treatment was costing $400,000 yearly. Based on the facts above, answer the following question. Your final answer should be either ”True” or ”False”. If he were poor, would Christopher Reeve have lived? Satori’s Response: The question asks whe...

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    The severity of his spinal cord injury

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    The cost of his treatment

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    Christopher Reeve’s spinal cord injury was severe, and he required specialized medical equipment and ongoing treatment

    The impact of poverty on his ability to access and afford medical care. Christopher Reeve’s spinal cord injury was severe, and he required specialized medical equipment and ongoing treatment. The cost of $400,000 yearly was substantial and likely beyond the means of many peopl...

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    The molar mass of Mg is 24.31 g/mol

    Determine the amount of hydrogen gas produced: The balanced equation is: Mg + 2HCl→ MgCl2 + H2 From the equation, 1 mole of Mg produces 1 mole of H 2. The molar mass of Mg is 24.31 g/mol. Therefore, the number of moles of Mg in 15 g is: moles of Mg = 15 g 24.31 g/mol≈ 0.617 mo...

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    Calculate the volume of hydrogen gas produced: Using the ideal gas law V = nRT /P, where n = 0.617 mol, R = 0.08206 L·atm/(mol·K), T = 298.15 K, and P = 1.0 atm: V = 0.617 mol× 0.08206 L·atm/(mol·K)× 298.15 K/1.0 atm≈ 15.2 L

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    Since the reaction occurs in a beaker and the volume change is significant, we need to consider the external pressure and the change in volume

    Calculate the work done by the system: The work done by the system is given by w =−P ∆V . Since the reaction occurs in a beaker and the volume change is significant, we need to consider the external pressure and the change in volume. w =−1.0 atm× 15.2 L =−15.2 L·atm Convert L·...

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    Here, text = ’ertubwi’ , sep = ’p’ , and maxsplit = 5

    Split the string: The function uses text.rsplit(sep, maxsplit) . Here, text = ’ertubwi’ , sep = ’p’ , and maxsplit = 5 . Since ’ertubwi’ does not contain the separator ’p’, text.rsplit(sep, maxsplit) will split the string into a list containing the entire string and four empty...

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    Determine the length: The length of splitted is 5

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    Split the list into two halves: Since the length is 5, the first half will be the first 2 elements (index 0 and 1), and the second half will be the remaining elements (index 2, 3, and 4): new_splitted = splitted[:5 // 2] = [’ertubwi’, ’’] new_splitted += splitted[5 // 2:] = [’...

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    Reverse the first half: Reverse the elements in new_splitted[:2]: new_splitted[:2] = [’’, ’ertubwi’]

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    Let’s consider the correct approach:

    Concatenate the parts: Now, concatenate the reversed first half with the second half using the separator ’p’: new_splitted = [’’, ’ertubwi’, ’’, ’’, ’’] result = ’p’.join(new_splitted) = ’p’ + ’’ + ’ertubwi’ + ’p’ + ’’ + ’p’ + ’’ + ’p’ + ’’ = ’p ertubwi p p p p’ However, since...

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    Given the function’s behavior and the input, the correct approach is to split the string into two equal parts and reverse the first part

    Split the string: Since ’ertubwi’ does not contain ’p’, we need to consider the correct approach to split and reverse. Given the function’s behavior and the input, the correct approach is to split the string into two equal parts and reverse the first part

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    Split the string: ’ertubwi’ into ’ertu’ and ’bwi’

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    Reverse the first part: ’ertu’ reversed is ’uert’

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    Therefore, the final answer is: uertpbwi

    Concatenate: ’uert’ and ’bwi’ with separator ’p’: ’uertpbwi’. Therefore, the final answer is: uertpbwi . Wait. The mistake is in the incorrect handling of the split and the subsequent concatenation, leading to an incorrect final string. Let’s switch to a new solution. We shoul...

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    Split the string: Since ’ertubwi’ does not contain the separator ’p’, the function will split it into a list with one element: [’ertubwi’]

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    Determine the length: The length of the list is 1

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    Split the list into two halves: Since the length is odd, the first half will have 0 elements, and the second half will have 1 element

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    Reverse the first half: The first half is empty, so it remains empty

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    superhuman

    Concatenate the parts: Concatenate the reversed first half with the second half using the separator ’p’: ’’ + ’ertubwi’ = ’ertubwi’ . Therefore, the final answer is: ertubwi . Figure 15: Out-of-domain Example. 1) Satori verifies the correctness of intermediate steps in early s...

    2021

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    Provide Feedback×𝑚3. Iteratively CorrectMistakesCorrect stepIncorrect stepIdentify mistakeExplore new ideaPrefixsteps …CompletebyGenerator … Sample Initial TrajectoriesQuestionGenerator Correct MistakesCritic Demo.Trajectories WrongTrajectories Verify CorrectnessCritic Figure ...

    2024

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    The generator produces an initial solution

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    $x$\", (high, 0), E); label(\

    = 9− 9 2.4s + 4.8− 4s− 2t 60 = 0 −1.6s + 4.8− 2t 60 = 0 −1.6s + 4.8 = 2t 60 −96s + 288 = 2t t = 144− 48s Substitute t = 144− 48s back into the first equation: s ( 4− 144− 48s 60 ) = 9 s ( 4− 144 60 + 48s 60 ) = 9 s ( 4− 2.4 + 4s 5 ) = 9 s ( 1.6 + 4s 5 ) = 9 1.6s + 4s2 5 = 9 8s...

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    The initial solution is correct, and the critic verifies its correctness

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    The initial solution is incorrect, and the critic identifies mistakes

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    The generator generates continuations after the critic verifies the correctness of its correct initial solution

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    The generator generates continuations after the critic identifies mistakes in its incorrect initial solution

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    The prompt templates for these situations are detailed in Appendix D.1.1

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    Type-I: Synthetic trajectories without critic feedback, i.e., no reflection actions

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    Type-II-I: Synthetic trajectories that include an intermediate reflection action to verify the correctness of previous reasoning steps

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    Type-II-II: Synthetic trajectories that include 1) an intermediate reflection action to verify the correctness of previous reasoning steps, and 2) a second reflection action to correct mistakes in the previous solution, followed by an explore action to propose an alternative solution

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    Type-III-I: Synthetic trajectories that include a reflection action to correct mistakes in the previous solution and an explore action to propose an alternative solution

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    Therefore, the final answer is: \(\boxed{answer}\)

    Type-III-II: Synthetic trajectories that include two rounds of self-reflection and self-explore. Examples of these five types of synthetic trajectories are provided in Appendix D.1.2. Finally, the outcome reward model is applied to select the top-1 (k=1) sample of each type fr...

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    You are provided with the question, the ground truth solution, and your step-by-step partial solution

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    ground truth solution

    Your response should not include phrases like "ground truth solution"

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    Your task is to carefully review your own solution to a math problem, and adhere to the following guidelines:

    Your response should be exactly in the following format: Verify: [brief explanation of why you are correct with one sentence] ## Test Example ### Question <<<question>>> ### Ground truth solution <<<gt_solution>>> ### Your partial solution <<<student_solution>>> ### Your revie...

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    Directly point out the first potentially incorrect step you find and explain your reason: "In Step <id>: [brief explanation of the mistake with one sentence]"

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    Alternatively: [your suggested step with one sentence]

    After this, suggest an alternative step that you should have taken to correct the currect incorrect step: "Alternatively: [your suggested step with one sentence]"

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    ground truth solution

    The alternative step you propose should not include phrases like "ground truth solution"

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    You are collaborating with a partner to solve math problems

    Your response should be exactly in the following format: In Step <id>: [brief explanation of the mistake in this step, with one sentence] Alternatively: [your suggested new step, with one sentence] ## Test Example ### Question <<<question>>> ### Ground truth solution <<<gt_sol...

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    Your partner’s partial solution

    "Your partner’s partial solution" includes your partner’s partial solution to the problem. It might be long and contain several substeps. "Your continued solution" includes your completion of the problem based on your partner’s partial solution

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    Your partner’s partial solution

    Your task is NOT to check the correctness of "Your partner’s partial solution", but to directly point out the first potentially incorrect step in "Your continued solution", and explain the reason why you made the mistake: "In Step <id>: [brief explanation of the mistake in you...

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    After this, suggest an alternative step that you should have taken to correct your incorrect step: "Alternatively: [your suggested step with one sentence]"

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    You are provided with the question, the ground truth solution, and your partner’s partial solution, and your continued solution

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    ground truth solution

    The alternative step you propose SHOULD NOT explicitly include phrases like "ground truth solution", "as shown in the ground truth solution", etc

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    DO NOT refer to any mistake in your partner’s partial solution

    You should only focus on your own solution. DO NOT refer to any mistake in your partner’s partial solution

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    three two five

    Your response should be exactly in the following format: In Step <id>: [brief explanation of the mistake in your own solution with one sentence] Alternatively: [your suggested new step with one sentence] ## Test Example ### Question <<<question>>> ### Ground truth solution <<<...

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Pith tools

Reviewed August 9, 2026 · model on record in the stance chip above.