LLMs have improved at executing well-specified chains of reasoning but remain weak at conceptual ideation, which identifies what is worth reasoning about in the first place. We cast this as bilevel optimization over (i) a compact hypothesis space 𝛩⊆𝛩₀ and (ii) a point 𝜃∈𝛩, and derive a domain-agnostic prompting strategy — Generate-𝛩 — that makes hypothesis-space construction an explicit pre-solving step. On two challenging puzzle domains, Generate-𝛩 matches or exceeds the max-thinking variant of the same base model (Claude Opus 4.6 or DeepSeek-v3.2/v4) and outperforms reasonable prompting baselines. These results suggest our method works well in tasks that are well-represented in the training set but nonetheless require creativity to solve new instances. Based on our formalism, we propose extensions for solving less familiar tasks as well. Results may provide insight into strategies learned by “reasoning” models during training. Our prompting strategy (or extensions thereof) could be integrated with RL training to produce better exploratory data for reasoning models in ideation-heavy tasks.