In information retrieval (IR), providing appropriate clarifications to better understand users' information needs is crucial for building a proactive search-oriented dialogue system. Due to the strong in-context learning ability of large language models (LLMs), recent studies investigate prompting methods to generate clarifications using few-shot or Chain of Thought (CoT) prompts. However, vanilla CoT prompting does not distinguish the characteristics of different information needs, making it difficult to understand how LLMs resolve ambiguities in user queries. In this work, we focus on the concept of ambiguity for clarification, seeking to model and integrate ambiguities in the clarification process. Following the reasoning and acting paradigm, we propose a new prompting scheme Ambiguity Type-Chain of Thought (AT-CoT), which enhances the reasoning abilities of LLMs by limiting CoT to first predict ambiguity types that can be interpreted as actions, then generate clarifications correspondingly. Experiments are conducted on various datasets containing human-annotated clarifying questions to compare AT-CoT with multiple baselines. We also perform user simulation to implicitly measure the quality of generated clarifications under various IR scenarios. Our codes are available at: https://github.com/anfutang/ClarifyingAmbiguities/.