Getting started with AI Gateway using a coding agent

Make a request to the Vercel AI Gateway to verify my API key works.

- Use cURL to POST to https://ai-gateway.vercel.sh/v1/responses
- Authenticate with a Bearer token using my AI_GATEWAY_API_KEY env var
- Use the model "anthropic/claude-sonnet-4.6"
- Send the prompt: "Invent a new holiday and describe its traditions."
- Run it and show me the response.

curl -X POST "https://ai-gateway.vercel.sh/v1/responses" \
  -H "Authorization: Bearer $AI_GATEWAY_API_KEY" \
  -H "Content-Type: application/json" \
  -d '{
    "model": "anthropic/claude-sonnet-4.6",
    "input": [
      {
        "type": "message",
        "role": "user",
        "content": "Invent a new holiday and describe its traditions."
      }
    ]
  }'

Create a TypeScript project that uses the AI SDK to stream a response
from Vercel AI Gateway.

- Initialize with pnpm and install the `ai` package, dotenv,
  @types/node, tsx, and typescript
- Store the API key in .env.local as AI_GATEWAY_API_KEY
- Use streamText with the model "openai/gpt-5.2"
- Stream the output to stdout, then log token usage and finish reason
- Run it with tsx to verify it works

Add AI Gateway to this project using the AI SDK.

- Install the `ai` package if not already installed
- Use my AI_GATEWAY_API_KEY from .env.local
- Models use the format "provider/model", for example "openai/gpt-5.2"