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Large language models are increasingly used for ideation, yet most interactions with them occur through linear GUI-based chat interfaces that favor incremental refinement over exploratory thinking. We introduce Tangible Prompting, a system that supports AI persona assisted ideation through the manipulation of physical objects representing different ideation actions, allowing users to navigate and shape a space of emerging ideas. The physical vocabulary externalizes diverse choices in an ideation process and enables users to generate alternatives, redirect exploration, combine ideas, and remove unpromising directions. Our study with 32 participants examined how pairs collaboratively ideate using the system with tangible interface compared to screen-only interface. The findings suggest that tangible interactions trigger more verbal communication between participants, give beat to a different rhythm of ideation, and contribute to an increased agency of human ideas over AI contributions