In this paper, we propose an agent-type LLM framework for AI systems that understand and recognize customer intent in domains characterized by short sentences and cold-start problems. To overcome the limitations of existing methods, we extend 36 general user intents to 278 fine-grained intents through hierarchical topic modeling and intent discovery, and generate synthetic user query data to augment real utterances and reduce the dependency on human annotations, especially in resource-poor environments. Through LLM-based topic modeling and strategic use of synthetic utterances, we improve the variability and coverage of the dataset, thereby presenting a comprehensive and powerful framework for discovering and recognizing novel customer intents online. In particular, we improve the quality and usability of synthetic queries through few-shot prompting, and show that intent descriptions and keywords generated by LLM can effectively replace those generated by humans.