Building effective LLM agents increasingly requires selecting appropriate AI models as tools from large open repositories (*e.g.*, HuggingFace with >2M models) based on natural language requests. Unlike invoking a fixed set of API tools, repository-scale model selection must handle massive, evolving candidates with incomplete metadata. Existing approaches incorporate full model descriptions into prompts, resulting in prompt bloat, excessive token costs, and limited scalability. To address these issues, we propose **HuggingR⁴**, the first framework to recast model selection as an iterative reasoning process rather than one-shot retrieval. By integrating **R**easoning, **R**etrieval, **R**efinement, and **R**eflection, HuggingR⁴ progressively decomposes user intent, retrieves candidates through multi-round deliberation, refines selections via fine-grained analysis, and validates results through reflection. To facilitate rigorous evaluation, we introduce a large-scale benchmark comprising 14,399 user requests across 37 task categories. Experiments demonstrate that HuggingR⁴ achieves 93.01% workability and 84.25% reasonability—outperforming state-of-the-art baselines by absolute margins of 17.81% and 23.13%, respectively, while reducing token consumption by 6.9×.