Conditional visibility based on a user specific document reference?

I'm trying to do something that I thought would be quite simple, but I can't quite seem to get my head around.

I have a collection of documents that a user can access. Once they have accessed this document, it is added as a reference in an array under their profile. All good so far.

But I want to control an element's visibility (a button) depending on whether they have accessed specific documents. If they have viewed 6 specific documents (which could be called by ID) then the visibility boolean should be toggled.

I can't seem to get the logic string working. Any suggestions gratefully received!