Vercel AI SDK Basic Chat Setup

Initialize a new Next.js project and integrate the Vercel AI SDK to create a basic streaming chat interface. Configure it to use OpenAI's `gpt-3.5-turbo` (or `o3`). Provide the necessary `api/chat/route.ts` and client-side component code.

```typescript
// api/chat/route.ts
import { createOpenAI } from '@ai-sdk/openai';
import { streamText } from 'ai';

const openai = createOpenAI({
  apiKey: process.env.OPENAI_API_KEY,
});

export async function POST(req: Request) {
  const { messages } = await req.json();

  const result = await streamText({
    model: openai('gpt-3.5-turbo'),
    messages,
  });

  return result.to Response();
}
```

```typescript
// app/page.tsx (or similar client component)
'use client';

import { useChat } from 'ai/react';

export default function Chat() {
  const { messages, input, handleInputChange, handleSubmit } = useChat();

  return (
    <div>
      {messages.map(m => (
        <div key={m.id}><b>{m.role}:</b> {m.content}</div>
      ))}

      <form onSubmit={handleSubmit}>
        <input
          value={input}
          placeholder="Say something..."
          onChange={handleInputChange}
        />
        <button type="submit">Send</button>
      </form>
    </div>
  );
}
```