Generative AI systems (GenAI) are increasingly used by students as learning companions, yet little is known about how they regulate these tools in open-ended learning settings, where the goal is to improve understanding for later independent performance. This study examined Grade-9 students' use of a general-purpose GenAI during mathematical-modeling practice through the lens of epistemic proactivity (EP)---the extent to which learners retain responsibility for regulating and advancing their own knowledge-building. We operationalized EP through two complementary behavioral dimensions: self-regulated learning (SRL) functions and help-seeking (HS) content. We asked whether static summaries of these behaviors or their within-session development were more informative about subsequent unaided performance. A total of 112 students interacted with a web-based LLM tutor, producing 880 substantive student turns; 95 completed both the unaided pre- and post-tests. Interactions were strongly request-dominated, with comparatively little explicit planning, monitoring, or evaluation, and students' stated HS intentions were only weakly reflected in their enacted behavior. Static summaries of AI use did not account for additional post-test variance beyond pre-test performance. In contrast, among the 89 students with HS computable trajectories, within-session HS development was informative: students whose requests became relatively more understanding-oriented---toward conceptual and procedural assistance rather than answer-seeking or verification---showed higher subsequent unaided performance. These findings suggest that AI-supported learning cannot be understood from aggregate interaction characteristics alone; the change in the depth with which students formulate their requests as an interaction develops may provide additional insight into their subsequent performance without AI.

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