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```javascript
/**
 * AI Dev Tool: AI-Native SaaS Vector Search API
 * 
 * This is a high-demand, production-ready developer code asset that integrates
 * PostgreSQL Vector Search Extension with a FastAPI + Supabase boilerplate.
 * 
 * It provides a research workspace where the agent can build its own panes and
 * performs AI tool calling using vanilla JavaScript.
 * 
 * @author Elite Software Architect and Micro-SaaS Developer
 */

// Import required dependencies
import { FastAPI } from 'fastapi';
import { SupabaseClient } from '@supabase/supabase-js';
import { Pool } from 'pg';
import { VectorSearch } from 'pg-vector-search';

// Define the FastAPI app
const app = new FastAPI();

// Define the Supabase client
const supabaseUrl = 'https://your-supabase-url.supabase.co';
const supabaseKey = 'your-supabase-key';
const supabase = new SupabaseClient(supabaseUrl, supabaseKey);

// Define the PostgreSQL pool
const postgresUrl = 'postgresql://your-postgres-username:your-postgres-password@your-postgres-host:your-postgres-port/your-postgres-database';
const pool = new Pool({
  connectionString:

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