This chapter connects how problems are defined to the modes of thinking they require, showing that accurate characterization is essential for effective framing and reframing. It introduces three interrelated dimensions—problem structure (structured, semi-structured, unstructured), hybrid type (familiar or novel; simple, complex, or wicked), and mode of thought (critical, creative, or both)—as a diagnostic lens for matching human cognition and AI collaboration to the real nature of a challenge. The chapter explains how problem movement, the way problems shift in form and difficulty over time, demands continual reassessment of these dimensions. Through sectoral examples in national security, business, and healthcare, it demonstrates how different hybrid problem types call for distinct balances of critical and creative thinking and corresponding human-AI engagement strategies. Leaders must guard against AI-induced suppression of these thinking modes and intentionally cultivate both. Ultimately, problem characterization serves as the bridge between understanding and action, ensuring framing remains aligned with a problem’s evolving structure and complexity. It equips leaders to recognize when to analyze, when to imagine, and how to keep human judgment and AI support dynamically aligned as problems move and reframe.