  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 integrated 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 10 popular math reasoning datasets, we demonstrate the
effectiveness of our proposed approach and thoroughly analyze the strengths of
each module. Moreover, empirical results suggest that our framework is
orthogonal to recent work that makes improvements on single reasoning methods
and can further generalise to logical reasoning domain. By allowing method
switching, XoT provides a fresh perspective on the collaborative integration of
diverse reasoning thoughts in a unified framework. The code is available at
https://github.com/tengxiaoliu/XoT.
