Hello @EnartisV ,
That sounds like a solid, straightforward workflow for re-engagement. I'd recommend checking out this article regarding contact engagements (including the pre-built segmentations), as it covers ways you can re-engage the lower level contacts. Once you've made your effort to re-engage them, give them time to interact with the button you're using to determine their interest. After they've had enough time to see the email and interact with it - maybe a week or two, depending on how often you send emails - you'll want to remove those contacts.
You can also create your own sort of least-engaged segmentation, beyond the pre-built algorithmic one. This way you can deliberately target contacts that haven't even opened your material in months or longer, and simply get rid of them if you don't believe they're worth the effort of trying to re-engage.
For an overview of the specific low-engagement segmentation
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