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Large language models (LLMs) are becoming increasingly applied beyond natural language processing, demonstrating strong capabilities in complex scientific tasks that traditionally require human expertise. This progress has extended into materials discovery, where LLMs introduce a new paradigm by leveraging reasoning and in-context learning, capabilities absent from conventional machine learning approaches. Here, we present a Multi-Agent-based Electrocatalyst Search Through Reasoning and Optimization (MAESTRO) framework in which multiple LLMs with specialized roles collaboratively discover high-performance single atom catalysts for the oxygen reduction reaction. Within an autonomous design loop, agents iteratively reason, propose modifications, reflect on results and accumulate design history. Through in-context learning enabled by this iterative process, MAESTRO identified design principles not explicitly encoded in the LLMs' background knowledge and successfully discovered catalysts that break conventional scaling relations between reaction intermediates. These results highlight the potential of multi-agent LLM frameworks as a powerful strategy to generate chemical insight and discover promising catalysts.