Zero-shot prompting techniques for mathematical reasoning can be applied to diverse datasets. However, these techniques necessitate large language models (LLMs) that encompass multiple capabilities, including problem comprehension, logical reasoning, and computational skills. Existing research primarily enhances prediction accuracy but remains vulnerable to errors stemming from deficiencies in these capabilities during the intermediate reasoning process. To improve the reliability of reasoning pathways, this paper introduces the React-Driven Skill Decision (RSD-ZP) framework, which automates the design of zero-shot prompts by integrating relevant skills which are different. This multi-stage prompting framework aims to mitigate errors associated with zero-shot prompting. Additionally, we propose Midcheck to enhance the execution success rate of methods within program reasoning chains. We conduct experiments on foundational reasoning methods, including Chain-of-Thought (COT) and Program-of-Thought (POT). Experimental results demonstrate that our proposed method significantly outperforms existing zero-shot prompting baselines on mathematical word problems (MWPs), while Midcheck notably reduces the execution error rate in the reasoning process.