Choose the Right Model-Based Tool for Three Different Systems

For each of the following systems, choose the most appropriate model-based technique from {decision-time MCTS, Dyna-style background planning, latent-space world-model agent trained mostly on imagined rollouts}, and justify your choice against the other two options:

1. A turn-based strategy game agent with a moderate branching factor (roughly 30 legal moves per turn) and an exact, fast simulator.
2. A simulated continuous-control robotics benchmark with high-dimensional camera pixel observations, where real (simulated) environment steps are somewhat expensive to compute relative to a learned latent model's forward pass.
3. A small-scale operations-research problem (e.g., a simple inventory-restocking simulator) with a low-dimensional, tabular state representation and a cheap-to-learn transition model.