Workflow to Push a Campaigns Contact to MH List

I see every other sync option available but the most obvious one! I'm trying to setup a workflow within Campaigns to add a contact to a MH List when the click something.

My problem is the MH List does not show up in the dropdown list. I'm putting this question here in MH forum because I'm trying to figure out how to automatically push a contact from Campaigns to MH.

Do we have to push back to CRM which then pushes to MH? I'm reading the documentation which doesn't mention it at all which to me would be the first thing to figure out how to do!

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