Synchronise inventory between Woocommerce and Local DB

I currently have a WooCommerce webstore and a point of sales (POS) system in my brick and mortar store.

What I would like to do is keep the inventory in sync each time a sale in made in either place.

What I currently have:

WP All Export plugin creates an .XML file each time a sales is make and saves it to to a URL.
The POS system creates a .XML file each time a sale is made and can push this to an external URL.
How can I use this information to keep my inventory in sync? Can I use webhooks to help with this or is there some other way that is best to do this. All I wish to do is keep the quantities in sync, nothing else.