Next Point-of-Interest (POI) recommendation is a fundamental task in location-based services. While recent advances leverage Large Language Model (LLM) for sequential modeling, existing LLM-based approaches face two key limitations: (i) strong reliance on the contextual completeness of user histories, resulting in poor performance on out-of-history (OOH) scenarios; (ii) limited scalability, due to the restricted context window of LLMs, which limits their ability to access and process a large number of candidate POIs. To address these challenges, we propose Tool4POI, a novel tool-augmented framework that enables LLMs to perform open-set POI recommendation through external retrieval and reasoning. Tool4POI consists of three key modules: preference extraction module, multi-turn candidate retrieval module, and reranking module, which together summarize long-term user interests, interact with external tools to retrieve relevant POIs, and refine final recommendations based on recent behaviors. Unlike existing methods, Tool4POI requires no task-specific fine-tuning and is compatible with off-the-shelf LLMs in a plug-and-play manner. Extensive experiments on three real-world datasets show that Tool4POI substantially outperforms state-of-the-art baselines, achieving up to 40% accuracy on challenging OOH scenarios where existing methods fail, and delivering average improvements of 20% and 30% on Acc@5 and Acc@10, respectively.