The synthesis of complex natural products remains one of the grand challenges of organic chemistry. We present DeepRetro, a major advancement in computational retrosynthesis that enables the discovery of viable synthetic routes for complex molecules typically considered beyond the reach of existing retrosynthetic methods. DeepRetro is a novel, open-source framework that tightly integrates large language models (LLMs), traditional retrosynthetic engines, and expert human feedback in an iterative design loop. Prior approaches rely solely on template-based methods or unconstrained LLM outputs. In contrast, DeepRetro combines the precision of template-based methods with the generative flexibility of LLMs, controlled by rigorous chemical validity checks and enhanced by recursive refinement. This hybrid system dynamically explores and revises synthetic pathways, guided by both algorithmic checks and expert chemist feedback through an interactive user interface. While DeepRetro achieves strong performance on standard retrosynthesis benchmarks, its true strength lies in its ability to propose novel, viable pathways to highly complex natural products-targets that have historically eluded automated planning. Through detailed case studies, we illustrate how this approach enables new routes for total synthesis and facilitates human-machine collaboration in organic chemistry. Beyond retrosynthesis, DeepRetro represents a working model for how to leverage LLMs in scientific discovery. We provide a transparent account of the system's design, algorithms, and human-feedback loop, enabling broad adaptation across scientific domains. By releasing DeepRetro as an open-source tool, we aim to empower chemists to tackle increasingly ambitious synthetic targets, accelerating progress in drug discovery, materials design, and beyond.