Medical order extraction from doctor-patient conversations presents a critical challenge in reducing clinical documentation burden and ensuring accurate capture of patient care instructions. This paper describes our system for the MEDIQA-OE 2025 shared task using the ACI-Bench and PriMock57 datasets, which achieved second place on the public leaderboard with an average score of 0.6014 across four metrics: description ROUGE-1 F1, reason ROUGE-1 F1, order-type strict F1, and provenance multi-label F1. Unlike traditional approaches that rely on fine-tuned biomedical language models, we demonstrate that a carefully engineered zero-shot prompting strategy using Gemini 2.5 Pro can achieve competitive performance without requiring model training or GPU resources. Our approach employs a deterministic state-machine prompt design incorporating chain-of-thought reasoning, self-verification protocols, and structured JSON output generation. The system particularly excels in reason extraction, achieving 0.4130 ROUGE-1 F1, the highest among the top performing teams. Our results suggest that advanced prompt engineering can effectively bridge the gap between general-purpose large language models and specialized clinical NLP tasks, offering a computationally efficient and immediately deployable alternative to traditional fine-tuning approaches with significant implications for resource-constrained healthcare settings.