Assistance from AI tools has supported and improved human performance across domains. However, recent research suggests that these immediate benefits may entail future costs, including diminished performance when AI assistance is no longer available. We study how human-AI interaction behaviors correlate with immediate and future unassisted task performance across two game-based problem-solving user studies ($n=139$ and $n=111$), using a \textit{dialogue act} framework adopted from a tutor-student dialogue taxonomy. In our studies, verbalizing thought processes correlates with higher unassisted outcomes, whereas directly requesting solutions correlates negatively. Similar to these participant-side patterns, assistant explanations of the current problem state are associated with better subsequent unassisted performance, whereas directly providing the next action is associated with worse performance. Qualitative and subtype analyses further show that ostensibly similar reasoning turns can elicit different assistance. Our findings suggest that preserving users' cognitive participation in problem-solving may support performance beyond AI-assisted interaction.

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