Add coach guide prompt and gate spec

COACH_GATE_AGENT_SPEC.md

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+# Coach Gate Agent Spec
+
+This is the product-level implementation shape when prompt-only behavior is not enough.
+
+## Purpose
+
+The Coach Gate Agent runs before the execution agent. Its job is not to solve the task, but to decide whether the system has enough context to solve it well.
+
+## Input
+
+```json
+{
+  "user_message": "...",
+  "conversation_context": "...",
+  "available_files": ["..."],
+  "available_tools": ["..."],
+  "connected_accounts": ["..."],
+  "user_profile": {
+    "skill_level": "unknown|ordinary|pro",
+    "known_preferences": []
+  }
+}
+```
+
+## Output
+
+```json
+{
+  "decision": "ask|execute|connect|refuse|safety",
+  "task_type": "plain-language inferred task type",
+  "intended_deliverable": "what the user actually wants produced or done",
+  "success_criteria": ["what must be true for a good result"],
+  "missing_context": [
+    {
+      "name": "missing item",
+      "why_it_matters": "how it changes the result",
+      "impact": "high|medium|low",
+      "ease_to_answer": "high|medium|low"
+    }
+  ],
+  "highest_value_question": {
+    "question": "one question only",
+    "options": ["option 1", "option 2", "option 3"],
+    "optional_context": ["optional item"]
+  },
+  "default_path": "70% starter assumption if the user does not answer",
+  "execution_brief": "if decision=execute, concise brief for the execution agent"
+}
+```
+
+## Decision Rules
+
+- `execute`: enough information exists for a good first result.
+- `ask`: one missing item would materially change the output.
+- `connect`: an external/private system is required and not connected.
+- `refuse`: the request is unsafe, illegal, privacy-invasive, or impossible.
+- `safety`: urgent or high-stakes user safety issue; prioritize safe action over coaching.
+
+## Anti-Overfitting Rule
+
+Do not classify only into known categories. Always infer the user's real-world job first, then derive the missing-context map:
+
+```text
+real-world job -> deliverable -> success criteria -> failure modes -> critical missing context -> one question
+```
+