Believing is a action of the mind friend, its a work!
According to scripture, it is not a work, DESPITE it being an action of the mind.
A work is something that you do to merit your salvation. Belief is a recognition that you CANNOT work to earn salvation, and therefore CANNOT be a work.
You're trying to make A = !A. It's illogical.
Thinking is action of the mind,
Not within the context of scripture it's not.