Replace 'YOUR_CLIENT_ID' and 'YOUR_API_KEY' with your actual Google API credentials. This example demonstrates a basic implementation of authorization and inbox cleanup using the Gmail API. It lists unread emails older than 7 days and marks them as read.

Please note that this code is a simplified example for demonstration purposes. Building a production-ready app would require error handling, better user feedback, and more comprehensive features for inbox management. Also, handling sensitive data like API keys securely is crucial.