Head out of the safe room and to the left, to the yet unopened door. In this new area, clear out the enemies and then use Third Eye for the first time. Move into the next hallway, through the door, and up the stairs. Here, Morgana should teach you have how to use cover, an incredibly useful tool for ambushing every enemy you come across.
Sneak your way down the hallway, taking out the enemies. Once you reach the end, take the door out. You will now be in a room with a cage and goat statues.