Definitely does NOT provoke AoO's.
Action Type Provoke AoO
Use spell-like ability Yes
Use supernatural ability No
Table Actions in Combat
It looks like, according to RAW, that you can use Abundant Step to get out of the grapple:
Grappled: A grappled creature is restrained by a creature, trap, or effect. Grappled creatures cannot move and take a –4 penalty to Dexterity. A grappled creature takes a –2 penalty on all attack rolls and combat maneuver checks, except those made to grapple or escape a grapple. In addition, grappled creatures can take no action that requires two hands to perform. A grappled character who attempts to cast a spell or use a spell-like ability must make a concentration check (DC 10 + grappler's CMB + spell level), or lose the spell. Grappled creatures cannot make attacks of opportunity.
A grappled creature cannot use Stealth to hide from the creature grappling it, even if a special ability, such as hide in plain sight, would normally allow it to do so. If a grappled creature becomes invisible, through a spell or other ability, it gains a +2 circumstance bonus on its CMD to avoid being grappled, but receives no other benefit.
EDIT: Although Abundant Step is a MOVE action so according to the grappled condition you would have to break the grapple first.
Well, the act of "casting" abundant step isn't a movement. I'd rule that you could, after all, not all move actions are movement.
