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This study adopts a distributed cognition perspective to examine the collaboration patterns and dynamics of college students when collaborating with AI for complex problem-solving. Through cluster analysis, three distinct collaborative problem-solving modes were identified: Delegated Reasoning (DR), Concerted Interpretation (CI), and Delegated Elaboration (DE). Findings further reveal that the DR group achieved the highest task performance, significantly outperforming the CI group. Additionally, the semantic similarity between human and AI discourse was notably the highest in the DR group. In contrast, the CI group reported significantly greater use of cognitive self-regulation strategies. These insights offer valuable implications for the future design of AI-assisted educational tools and student-AI collaborative learning frameworks.