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The quest is a subquest of Reunions and is the scripted dialogue scene that plays out between the player character, Piper Wright and Nick Valentine. Depending on whether or not Nick is with the player character when Conrad Kellogg is killed, this scene plays out either in Publick Occurences or the Valentine Detective Agency.
Thus player characters will automatically start and conclude this quest at the end of Reunions at which point Dangerous Minds will begin. This quest merely serves as a transition between those other two. For this reason, it never appears in the quest list or Pip-Boy, as it has no additional objectives.