Generative AI chatbots enable personalized problem-solving, but effective learning requires students to self-regulate both how they seek help and how they use AI-generated responses. Considering engagement modes across these two actions reveals nuanced reliance patterns: for example, a student may actively engage in help-seeking by clearly specifying areas of need, yet engage passively in response-use by copying AI outputs, or vice versa. However, existing research lacks systematic tools for jointly capturing engagement across help-seeking and response-use, limiting the analysis of such reliance behaviors. We introduce RelianceScope, an analytical framework that characterizes students' reliance on chatbots during problem-solving. RelianceScope (1) operationalizes reliance into nine patterns based on combinations of engagement modes in help-seeking and response-use, and (2) situates these patterns within a knowledge-context lens that accounts for students' prior knowledge and the instructional significance of knowledge components. Rather than prescribing optimal AI use, the framework enables fine-grained analysis of reliance in open-ended student-AI interactions. As an illustrative application, we applied RelianceScope to analyze chat and code-edit logs from 79 college students in a web programming course. Results show that active help-seeking is associated with active response-use, whereas reliance patterns remain similar across knowledge mastery levels. Students often struggled to articulate their knowledge gaps and to adapt AI responses. Using our annotated dataset as a benchmark, we further demonstrate that large language models can reliably detect reliance during help-seeking and response-use. We conclude by discussing the implications of RelianceScope and the design guidelines for AI-supported educational systems.

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