Sync posts via JSON API

We have a custom post type Events on our Wordpress website. Every event has a title, description and date.

From our CRM-system, we can create a JSON feed where we list all Events. Every event in the feed will have a unique ID, title, description and date.

Now we want to set up a sync from the CRM Wordpress system. In general:

• Automatically sync every x hours the data from CRM to Wordpress
• If an Event does not yet exist in Wordpress, but exists in CRM, then create the Event in Wordpress
• If an Event exists Wordpress and in CRM, then sync the Event data
• If an Event exists in Wordpress, but not in the JSON, then delete the event in Wordpress

Thank you.