To take down over a dozen of these robotic enemies, you'll have two options. This will unfortunately summon a hoard of Synths. Use the terminal to bring power back to the room. Drop down to the bottom floor and head through the hallway. Since the power is out, you won't be able to reach the higher area in the room. Keep heading further down until you reach the engine room. And don't forget to grab the Telsa Science magazine in the room before the turrets! If you read the terminal, there will be turrets installed in the lower levels that will fire at anyone without an employee badge. With all the enemies cleared, continue following Danse as you head further down into the building. Once opened, a group of Synths will appear on the other side, so get ready for a fight! If you don't have any energy based Weapons, grab one from a dead Synth and use that! Open it using the terminal opposite of the door.
Go downstairs to find a room with a locked door.
There is a terminal with information on the company in the second room you enter. In order to progress through the mission, you'll have to listen and talk to Danse whenever the marker appears above him.