Intent-aware session recommendation (ISR) is pivotal in discerning user intents within sessions for precise predictions. Traditional approaches, however, face limitations due to their presumption of a uniform number of intents across all sessions. This assumption overlooks the dynamic nature of user sessions, where the number and type of intentions can significantly vary. In addition, these methods typically operate in latent spaces, thus hinder the model's transparency.Addressing these challenges, we introduce a novel ISR approach, utilizing the advanced reasoning capabilities of large language models (LLMs). First, this approach begins by generating an initial prompt that guides LLMs to predict the next item in a session, based on the varied intents manifested in user sessions. Then, to refine this process, we introduce an innovative prompt optimization mechanism that iteratively self-reflects and adjusts prompts. Furthermore, our prompt selection module, built upon the LLMs' broad adaptability, swiftly selects the most optimized prompts across diverse domains. This new paradigm empowers LLMs to discern diverse user intents at a semantic level, leading to more accurate and interpretable session recommendations. Our extensive experiments on three real-world datasets demonstrate the effectiveness of our method, marking a significant advancement in ISR systems.