Using is both a noun AND a verb, in different respects.
It acts as a verb in the subordinate clause. Here it bears the same sense as a finite verbform of USE, and it ‘licenses’ (permits) the same complements which a finite verbform would license:—a Subject, a Direct Object, and an (optional) infinitival Predicative Complement designating the goal of the action. (In this particular case, the Subject is not specified; it is inferred to be ‘we’, the President and his hearers, ‘the nation’.) It is not, however, marked with tense; in effect it ‘borrows’ its tense from the main clause: a non-past form with future reference.
It acts as a noun in the superordinate main clause: specifically, it acts as the Direct Object of the main-clause verb advocate. (At least that is the ‘traditional’ parsing; some more contemporary grammars say that it acts as the head of a nonfinite clause and that it is the clause which acts as Direct Object of advocate.)
This ‘double use’ as a verb at one syntactic level and a noun at another is precisely what the term gerund signifies. Similarly, when an -ing form acts as both a verb and an adjective, it is called a participle.