Addressing inverse design problems in engineering often requires managing complex challenges. Traditionally such systems are optimized by manually setting up a model in a numerical simulation software and applying parameter optimization. Topology changes and variable parameter sets result in challenging mixed-integer optimization problems. Such problems are hard to solve automatically, that's why they normally need to be initialized manually with high effort by the design engineer. Generative probabilistic models, like Large Language Models (LLMs), can efficiently produce diverse, valid design concepts that are fully parameterizable, simulatable, and optimizable. We introduce cGenEDA a Virtual Design Expert-a system based on multiple LLM agents using in-context prompting to coordinate these tasks-providing a seamless, adaptable toolchain for automated design generation, optimization problem definition, and design automation. Our approach demonstrates that long, interacting code sequences can be generated and directly applied in domain-specific applications for precise forward simulations, setting up the optimization problem and combined with wellknown, black-box optimization algorithms, to efficiently solve inverse design problems.