Google Calendar Integration with AI Assistant

I am new to this but have created my AI assistant on VAPI, it's an American based company as i could not find a UK based company to do it through (maybe you know of some?) . My assistant it an AI receptionist for dental clinics, it is built to answer general questions , opening times etc but its main objective is to check, book and cancel appointments. I need help connecting it to a calendar so it can carry out the task.

I need help integrating my Google Calendar with my existing AI assistant. The AI should be able to check availability, book, and cancel appointments.

Ideal Skills and Experience:
- Experience with Google Calendar API
- Familiarity with AI assistant platforms
- Strong background in software integration

Please provide a brief overview of your relevant experience and approach to this task.