Training LLMs to orchestrate multi-step tool calls is held back by three coupled obstacles: realistic stateful execution environments are costly to build, synthetic training queries are often detached from the server's actual state (so the generated tool calls fail to execute), and recall-based RL rewards incentivize verbose tool-calling patterns. We present PROVE (Programmatic Rewards On Verified Environments), a framework with three contributions: (1) a library of 20 stateful MCP (Model Context Protocol) servers exposing 343 tools, enabling live-execution RL training with session-scoped state isolation; (2) a state-machine data synthesis pipeline that generates multi-turn tool-call trajectories grounded in live-sampled server state, so generated queries reference entities that actually exist; and (3) a multi-component programmatic reward with an adaptive efficiency penalty that counters the verbosity incentive of recall-based rewards. We train four models (Qwen3-4B, Qwen3-8B, Qwen2.5-7B, Granite-4.1-8B) with GRPO on the resulting ~13K training examples. On BFCL Multi-Turn, tau2-bench, and T-Eval, PROVE yields improvements of up to +10.2, +6.8, and +6.5 points respectively, demonstrating that this framework yields consistent gains on multi-step tool orchestration across two model families.