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The impacts of Generative Artificial Intelligence (GAI) on students' thinking processes remain largely unexplored. This research explores the thinking processes of 20 students when programming with the support of GAI. Participants recorded their screens for an hour-long programming session and submitted reflection reports. We developed an AI-augmented thinking coding framework with four stages: Question Formulation, Solution Generation, Solution Analysis and Evaluation, and Solution Refinement. Based on the time ratio of human-generating code versus copying code from GAI, participants were categorized into AI-lead (n=10) and human-lead (n=10) groups. Results of sequential pattern mining and case analysis indicated that the AI-lead group treated GAI as a leader, over-relying on it, while the human-lead group utilized it as a tool to optimize efficiency.