Large language models have advanced rapidly, from pattern recognition to emerging forms of reasoning, yet they remain confined to linguistic simulation rather than grounded understanding. They can produce fluent outputs that resemble reflection, but lack temporal continuity, causal feedback, and anchoring in real-world interaction. This paper proposes a complementary approach in which reasoning is treated as a relational process distributed between human and model rather than an internal capability of either. Building on recent work on "System-2" learning, we relocate reflective reasoning to the interaction layer. Instead of engineering reasoning solely within models, we frame it as a cognitive protocol that can be structured, measured, and governed using existing systems. This perspective emphasizes collaborative intelligence, combining human judgment and contextual understanding with machine speed, memory, and associative capacity. We introduce "The Architect's Pen" as a practical method. Like an architect who thinks through drawing, the human uses the model as an external medium for structured reflection. By embedding phases of articulation, critique, and revision into human-AI interaction, the dialogue itself becomes a reasoning loop: human abstraction -> model articulation -> human reflection. This reframes the question from whether the model can think to whether the human-AI system can reason. The framework enables auditable reasoning traces and supports alignment with emerging governance standards, including the EU AI Act and ISO/IEC 42001. It provides a practical path toward more transparent, controllable, and accountable AI use without requiring new model architectures.