One of the limitations of free Calendly account is that we can't receive instant appointment booked or cancelled notification through webhook.

But we can simple ask the user after certain time if they clicked the Calendly button. If we can have the email which they booked appointment with.
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You can actually pull all the appointment details(event name, zoom link, cancel url, reschedule url, event start & end time) all back into messenger. 

Then you can easily set up the reminder, reconfirmation, follow up automation.

Watch this video multiple times if it's required.

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