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Natural language chain-of-thought (N-CoT) and Program chain-of-thought (P-CoT) have emerged as two primary paradigms for large language models (LLMs) to solve mathematical problems. Current researches typically endeavor to unidirectional enhancement: P-CoT enhanced N-CoT or N-CoT enhanced P-CoT. In this paper, we seek to fully unleash the two paradigms' strengths for mutual enhancement, and ultimately achieving simultaneous improvement. We conduct a detailed analysis of error types of these two paradigms, based on which we propose Parrot, a novel training pipeline for mathematical problems: 1) Three target-designed subtasks integrate the sequential P-CoT and N-CoT generation. 2) A subtask hybrid training strategy to facilitate natural language semantic transferability. 3) The converted N-CoT auxiliary reward design to alleviate the sparse rewards in P-CoT optimization. Extensive experiments demonstrate that Parrot significantly enhances both the performance of N-CoT and P-CoT, especially on N-CoT. Using Parrot SFT, the LLaMA2 and CodeLLaMA's N-CoT performance even achieve +21.87 and +21.48 on MathQA over the RL baseline, which is resource-intensive.