On to the third badge | Walkthrough Pokemon X/Y Guide

Out of Geosenge, proceed through Road 11 to reach a cave in the north, go inside. In the cave You will, as always, encounter wild pokemon and trainers. Get to it!. Go south then east for stairs. Keep walking and fight the trainers. Head north once You find an exit and go through it. You're back on the first level. Just a few steps north, and You can get out. As You notice, now You can push the boulder south to You. If You want to return to the cave, or back to Geosenge, us a 'strength' taught Pokemon to push it (You can teach Pokemon a move by activating it in the menu).