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That point is fairly far into the current story. There are a few things you have to do in order to progress that far. Opening the lake and then visiting it in the morning to talk to the groundskeeper, getting the groundskeeper to take you to where he found the previous headmaster, talking to the science teacher to gain access to all of the old headmaster's files on the computer. I believe there may be a few more steps, but those are the ones I remember off the top of my head.
Yes. You have to continue the quest to find out what happened to the previous headmaster. Open the lake and talk to the groundskeeper in the morning, and eventually the quest will progress. It happens after a certain point in the rest of the story, but I can't remember exactly when. Also, if you haven't already started discipline training Claire, you should start doing that as well, as there is more story that is locked behind that as well.