# Exploring Extrinsic and Intrinsic Properties for Effective Reasoning with Code Interpreter

arXiv: https://arxiv.org/abs/2606.16934 · HTML: https://mlsanity.com/paper/2606.16934/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Reasoning for agents, planning and code, one of 17 directions in LLM reasoning.
- Builds on 17 of its 48 references that are in the map.
- First posted on arXiv 15 Jun 2026.

## Placed in

- LLM reasoning / [Reasoning for agents, planning and code](https://mlsanity.com/lr/reasoning-for-agents-planning-and-code/)

## Builds on (most cited first, 17 of 17)

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- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [Qwen3 Technical Report](https://mlsanity.com/paper/2505.09388/) (2025)
- [ReAct: Synergizing Reasoning and Acting in Language Models](https://mlsanity.com/paper/2210.03629/) (2022)
- [Qwen2.5 Technical Report](https://mlsanity.com/paper/2412.15115/) (2024)
- [Toolformer: Language Models Can Teach Themselves to Use Tools](https://mlsanity.com/paper/2302.04761/) (2023)
- [PAL: Program-aided Language Models](https://mlsanity.com/paper/2211.10435/) (2022)
- [A Survey on Test-Time Scaling in Large Language Models: What, How, Where, and How Well?](https://mlsanity.com/paper/2503.24235/) (2025)
- [ToRL: Scaling Tool-Integrated RL](https://mlsanity.com/paper/2503.23383/) (2025)
- [Olmo 3](https://mlsanity.com/paper/2512.13961/) (2025)
- [Grounded Reinforcement Learning for Visual Reasoning](https://mlsanity.com/paper/2505.23678/) (2025)
- [Does Thinking More always Help? Mirage of Test-Time Scaling in Reasoning Models](https://mlsanity.com/paper/2506.04210/) (2025)
- [Test-Time Scaling in Reasoning Models Is Not Effective for Knowledge-Intensive Tasks Yet](https://mlsanity.com/paper/2509.06861/) (2025)
- [Understanding Reasoning in LLMs through Strategic Information Allocation under Uncertainty](https://mlsanity.com/paper/2603.15500/) (2026)
- [It's Not That Simple. An Analysis of Simple Test-Time Scaling](https://mlsanity.com/paper/2507.14419/) (2025)

## Abstract (arXiv)

Reasoning with a Code Interpreter (CI) has emerged as an effective paradigm for enhancing the reasoning capabilities of large language models (LLMs) through executable computation and iterative verification. Despite its growing adoption, the behavioral properties underlying effective code reasoning remain largely underexplored. In this work, we investigate code reasoning from two distinct perspectives inspired by prior studies of natural language reasoning: extrinsic properties, represented by crucial tokens, and intrinsic properties, represented by code-specific cognitive behaviors. Across multiple LLMs, we find that stronger CI reasoning models consistently exhibit a higher prevalence of crucial tokens and cognitive behaviors, particularly verification, backtracking, and backward chaining. Building on these observations, we examine how these properties can be leveraged during both inference and training. At inference time, appending code-specific crucial tokens improves performance on several reasoning capabilities, including mathematical, ordering, and optimization, while yielding limited benefits elsewhere. At training time, augmenting a state-of-the-art framework with code-specific cognitive behaviors improves supervised fine-tuning and reinforcement learning performance in two of three evaluated models. Further analysis shows that these behaviors reduce overthinking in incorrect responses and improve token efficiency, while also revealing factors that limit gains in a certain model. Our findings provide the first systematic characterization of effective reasoning with CI and demonstrate both the potential and limitations of leveraging key properties to improve CI-based reasoning.