Large Action Models (LAMs) select and execute actions from external tool spaces. Traditional relevance-based retrieval selects actions that satisfy semantic relevance but violate execution constraints, parameter requirements, or action preconditions. Reactive execution discovers infeasible action orderings only during rollout, which increases replanning cost. Reliable multi-step execution therefore requires feasibility-aware selection and dependency-aware ordering. We propose ActionRAG, a training-free retrieval framework that combines Constraint Induction, Constraint-Aware Retrieval, and Action-of-Thought to select and order feasible actions before execution. Constraint Induction extracts environment-level and task-level constraints from the environment state and the user goal. Constraint-Aware Retrieval ranks actions by semantic relevance and feasibility coverage, filtering infeasible actions before trajectory construction. Action-of-Thought then constructs feasible action trajectories over the filtered action set using inter-action dependencies and preconditions. We evaluate ActionRAG on StableToolBench and MCP-Bench across four backbones under single-tool, multi-step, and cross-category tool-use settings. On StableToolBench, ActionRAG improves the solvable pass rate by 40.3–43.4%p over CoT/ReAct, reaching 60.7%p on cross-category tasks, and reduces token cost by up to 6.2× over DFSDT.