This quest is triggered at the immediate conclusion of Ad Victoriam. Now that you've found yourself inside The Institute, talk to Elder Maxson with your orders. He will also give you an important device: a fusion charge pulse.
Head to the reactor as indicated by the waypoint. Unsurprisingly, The Institute has locked down the Advanced Systems lab entrance leading to the reactor.
Take a detour up to Father's room and access the nearby terminal to override the lockdown. When you've finally made it inside the Advanced Systems lab, head toward the reactor chamber. Reach the reactor and activate it. Proctor Ingram will teleport you back to the relay room, after which you'll need to speak with Maxson and rescue the Synth version of Shaun. Step into the relay once more. Activate the detonator to finish off The Institute, and then speak with Maxson to complete the quest.
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