Belief comes from the Greek word pisteuo (which we translate as believe - the act) which means “to have faith (in, upon, or with respect to, a person or thing), i.e. credit; by impl. to entrust (espec. one’s spiritual well-being to Christ) :—believe (-r), commit (to trust), put in trust with.”
So it’s an active trust - not merely mental assent. As you sit in a chair, you put your trust in it as you plop down. That’s a fairly good metaphor for the kind of trust “believe” carries with it. If one’s belief does not affect one’s behavior, it merely assent and not a true belief.
Are we not called to be apostles, to pick up our crosses and follow Him? Stop for a second and think: the Apostles believed, how did that affect their behavior? Was their preaching, their travel, their suffering, their teaching, their healing, their anointing, their baptizing etc. works of the law or works of grace? Did what they did in the name of Christ mean that the Crucifix was not enough to save?
Belief is not just trust, it is action, remember, we are to take up our cross and follow Him, that is action. The importance of cooperating with grace by doing the good works of Christ is reflected in the first non-Gospel book listed in the NT; Acts of the Apostles. Works are not a product of faith, faith and works are a product of grace. And if you don't think works of grace are necessary for salvation, you may find your self in the uncomfortable position of asking "when did I see You..."
The dangerous, man made, unscriptural notion of sola fide is one of the devils greatest hits. ( so is the notion that one can get to heaven by "being a 'good' person, with out all that 'silly religious stuff')