The Collaborative International Dictionary of English v.0.48:

Advertent \Ad*vert"ent\, a. [L. advertens, -entis, p. pr. of
   advertere. See Advert.]
   Attentive; heedful; regardful. --Sir M. Hale. --
   Ad*vert"ent*ly, adv.
   [1913 Webster]

WordNet (r) 3.0 (2006):

advertently
    adv 1: in a careful deliberate manner [syn: mindfully,
           heedfully, advertently] [ant: inadvertently,
           unknowingly, unmindfully, unwittingly]