Word games hold significant research value for natural language processing (NLP), game theory, and related fields due to their rule-based and situational nature. This study explores how large language models (LLMs) can be effectively involved in word games and proposes a training-free framework. "Shei Shi Wo Di" or "Who is the Spy" in English, is a classic word game. Using this game as an example, we introduce a Chain-of-Thought (CoT)-based scheduling framework to enable LLMs to achieve excellent performance in tasks such as inferring role words and disguising their identities. We evaluate the framework's performance based on game success rates and the accuracy of the LLM agents' analytical results. Experimental results affirm the framework's effectiveness, demonstrating notable improvements in LLM performance across multiple datasets. This work highlights the potential of LLMs in mastering situational reasoning and social interactions within structured game environments. Our code is publicly available at https://github.com/ct-wei/Who-is-The-Spy.