The powerful reasoning and generative capabilities of large language models (LLMs) have inspired researchers to apply them to reasoning-based recommendation tasks, which require in-depth reasoning about user interests and the generation of recommended items. However, previous reasoning-based recommendation methods have typically performed inference within the language space alone, without incorporating the actual item space. This has led to over-interpreting user interests and deviating from real items. Towards this research gap, we propose performing multiple rounds of grounding during inference to help the LLM better understand the actual item space, which could ensure that its reasoning remains aligned with real items. Furthermore, we introduce a user agent that provides feedback during each grounding step, enabling the LLM to better recognize and adapt to user interests. Comprehensive experiments conducted on three Amazon review datasets demonstrate the effectiveness of incorporating multiple groundings and feedback. These findings underscore the critical importance of reasoning within the actual item space, rather than being confined to the language space, for recommendation tasks.