Radiation therapy treatment planning is an iterative, expertise-dependent process, and the growing burden of cancer cases has made reliance on manual planning increasingly unsustainable, underscoring the need for automation. In this study, we propose a workflow that leverages a large language model (LLM)-based agent to navigate inverse treatment planning for intensity-modulated radiation therapy (IMRT). The LLM agent was implemented to directly interact with a clinical treatment planning system (TPS) to iteratively extract intermediate plan states and propose new constraint values to guide inverse optimization. The agent's decision-making process is informed by current observations and previous optimization attempts and evaluations, allowing for dynamic strategy refinement. The planning process was performed in a zero-shot inference setting, where the LLM operated without prior exposure to manually generated treatment plans and was utilized without any fine-tuning or task-specific training. The LLM-generated plans were evaluated on twenty head-and-neck cancer cases against clinical manual plans, with key dosimetric endpoints analyzed and reported. The LLM-generated plans achieved comparable organ-at-risk (OAR) sparing relative to clinical plans while demonstrating improved hot spot control (Dmax: 106.5% vs. 108.8%) and superior conformity (conformity index: 1.18 vs. 1.39 for boost PTV; 1.82 vs. 1.88 for primary PTV). This study demonstrates the feasibility of a zero-shot, LLM-driven workflow for automated IMRT treatment planning in a commercial TPS. The proposed approach provides a generalizable and clinically applicable solution that could reduce planning variability and support broader adoption of AI-based planning strategies.