arXiv:2508.13172v1 Announce Type: cross Abstract: Analog IC design is a bottleneck due to its reliance on experience and inefficient simulations, as traditional formulas fail in advanced nodes. Applying Large Language Models (LLMs) directly to this problem risks mere "guessing" without engineering principles. We present a "synergistic reasoning" framework that integrates an LLM's strategic reasoning with the physical precision of the gm/Id methodology. By empowering the LLM with gm/Id lookup tables, it becomes a quantitative, data-driven design partner. We validated this on a two-stage op-amp, where our framework enabled the Gemini model to meet all TT corner specs in 5 iterations and extended optimization to all PVT corners. A crucial ablation study proved gm/Id data is key for this efficiency and precision; without it, the LLM is slower and deviates. Compared to a senior engineer's design, our framework achieves quasi-expert quality with an order-of-magnitude improvement in efficiency. This work validates a path for true analog design automation by combining LLM reasoning with scientific circuit design methodologies.