Comma before 'and' in adjectival phrase

I am struggling with whether the following should have a comma or not:

• The details we have can be linked to and used for your profile.

or

• The details we have can be linked to, and used for your profile.

My instinct would be without a comma; however, I cannot find a rule for this after searching online.

Concerning the title of this post, I was not sure about how to describe the elements in question here, so please forgive me if these are not examples of adjectival phrases. Not knowing this may well have led me to stuggle to find an answer.

Any help here would be greatly appreciated.