Planning computes a sequence of actions that transforms an initial state into a goal state. Classical search methods include breadth-first search, A*, heuristic search, and constraint-based planning, while modern systems often combine these with language-model-generated candidates.

A planner explores a search space defined by states, transitions, and costs. If $g(n)$ is the cost-to-come and $h(n)$ is a heuristic estimate of remaining cost, A* evaluates nodes with $f(n)=g(n)+h(n)$. Admissible heuristics preserve optimality under standard conditions.

In LLM-based agents, planning may occur through explicit task decomposition, tree search over candidate solutions, program synthesis, or tool invocation. The best systems verify or revise plans using external feedback and environmental checks.