Recent advances in mathematical problem-solving with language models (LMs) integrate chain-of-thought (CoT) reasoning and code execution to harness their complementary strengths. However, existing hybrid frameworks exhibit a critical limitation: they depend on externally dictated instructions or rigid code-integration templates, lacking metacognitive awareness—the capacity to dynamically evaluate intrinsic capabilities and autonomously determine when and how to integrate tools. This rigidity motivates our study of autonomous code integration, enabling models to adapt tool-usage strategies as their reasoning abilities evolve during training.While reinforcement learning (RL) shows promise for boosting LLM reasoning at scale (e.g., DeepSeek-R1), we demonstrate its inefficiency in learning autonomous code integration due to inadequate exploration of the vast combinatorial space of CoT-code interleaving patterns. To address this challenge, we propose a novel Expectation-Maximization (EM) framework that synergizes structured exploration (E-step) with off-policy RL optimization (M-step), creating a self-reinforcing cycle between metacognitive tool-use decisions and evolving capabilities. Experiments reveal our method achieves superior results through improved exploration. Notably, our 7B model improves over 11% on MATH500 and 9.4% on AIME without o1-like CoT.

Program-of-Thought (PoT) replaces natural language-based Chain-of-Thought (CoT) as the most popular method in Large Language Models (LLMs) mathematical reasoning tasks by utilizing external tool calls to circumvent computational errors. However, our evaluation of the GPT-4 and Llama series reveals that using PoT introduces more reasoning errors, such as incorrect formulas or flawed logic, compared to CoT. To address this issue, we propose Human-Think Language (HTL), which leverages a suite of strategies that help integrate PoT and CoT, encompassing: (1) a new generation paradigm that uses full CoT reasoning to control code generation. (2) Focus Attention, that directs model attention to the CoT reasoning during PoT to generate more logical code. (3) reinforcement learning that utilizes the accuracy of both CoT and PoT responses as rewards to prevent repetitive reasoning steps in LLMs when solving difficult math problems. Our method achieves an average improvement of 6.5% on the Llama-Base model and 4.3% on the Mistral-Base model across 8 mathematical calculation datasets. It also shows significant effectiveness on five out-of-domain datasets by controlling the model’s information flow, exhibiting strong transferability. Additionally, HTL shows the most significant improvement in non-mathematical natural language inference task, contributing to a unified reasoning task framework.