Books the job, and only says so when it did
It reads your actual calendar before it offers you a time.
When a caller asks about Tuesday, the receptionist opens your calendar and looks. If the window is free it offers it, books it, and sends the confirmation. If something overlaps it says so, and offers what is open instead.
The third case is where most AI booking falls over. If it cannot read your calendar right then, because the connection dropped or the request timed out, it is not allowed to guess. It tells the caller it cannot see the calendar and takes the request down instead. It never says a time is open when it did not check, and it only says "booked" when a real calendar event came back. A confident guess about your Tuesday is worse than an honest maybe.
