In the same sense as you say, "To love is a work, to believe is a work, to hope is a work", I also say, "to believe" is a work (a deed). Because, without performing the deed, then one cannot be in possession of a title. For one to be a believer, they must first perform 'to believe'.
OIC, the word 'faith' can be a noun or a verb. As a noun, 'faith' means one's religious system, as a verb, it means, 'to place confidence into someone, something'.