feat(actions): add plan, update done & web search

src/lib/agents/search/researcher/actions/plan.ts

@@ -0,0 +1,26 @@
+import z from 'zod';
+import { ResearchAction } from '../../types';
+
+const schema = z.object({
+  plan: z
+    .string()
+    .describe(
+      'A concise natural-language plan in one short paragraph. Open with a short intent phrase (e.g., "Okay, the user wants to...", "Searching for...", "Looking into...") and lay out the steps you will take.',
+    ),
+});
+
+const planAction: ResearchAction<typeof schema> = {
+  name: '___plan',
+  description:
+    'Use this FIRST on every turn to state your plan in natural language before any other action. Keep it short, action-focused, and tailored to the current query.',
+  schema: schema,
+  enabled: (_) => true,
+  execute: async (input, _) => {
+    return {
+      type: 'reasoning',
+      reasoning: input.plan,
+    };
+  },
+};
+
+export default planAction;