Large language models (LLMs) are increasingly shaping creative work and problem-solving; however, prior research suggests that they may diminish unassisted creativity. To address this tension, a coach-like LLM environment was developed that embodies divergent and convergent thinking personas as two complementary processes. Effectiveness and user behavior were assessed through a controlled experiment in which participants interacted with either persona, while a control group engaged with a standard LLM providing direct answers. Notably, users' perceptions of which persona best supported their creativity often diverged from objective performance measures. Trait-based analyses revealed that individual differences predict when people utilize divergent versus convergent personas, suggesting opportunities for adaptive sequencing. Furthermore, interaction patterns reflected the design thinking model, demonstrating how persona-guided support shapes creative problem-solving. Our findings provide design principles for creativity support systems that strike a balance between exploration and convergence through persona-based guidance and personalization. These insights advance human-AI collaboration tools that scaffold rather than overshadow human creativity.

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