触发：当需要计数、枚举、发现有限结构中的规律、或处理离散对象时调用。 科研模式：组合计数、图论分析、生成函数计算。 生活模式：系统性枚举、鸽巢推理、组织有限选项。 English: Trigger when you need to count, enumerate, find patterns in finite structures, or handle discrete objects. Research mode: combinatorial counting, graph theory analysis, generating function computation. Life mode: systematic enumeration, pigeonhole reasoning, organizing finite options.