As large language models (LLMs) have shown effectiveness with different prompting methods, such as Chain of Thought, Program of Thought, we find that these methods have formed a great complementarity to each other on math reasoning tasks. In this work, we propose XoT, an automatic problem solving framework by prompting LLMs with diverse reasoning thoughts. For each question, XoT always begins with selecting the most suitable method then executes each method iteratively. Within each iteration, XoT actively checks the validity of the generated answer and incorporates the feedback from external executors, allowing it to dynamically switch among different prompting methods. Through extensive experiments on 9 popular math reasoning datasets, we demonstrate the effectiveness of our proposed approach and thoroughly analyze the strengths of each module. Furthermore, empirical results suggest that our framework is orthogonal to recent work that makes improvements on single reasoning methods. By allowing method switching, XoT provides a fresh perspective on the collaborative integration of diverse reasoning thoughts in a unified framework.