I'm at the pedestal in the icy room. I'm holding the home plate shaped tablet. I've been all around--in the room with two bridges, for example--but I keep ending up here. Am I supposed to carry the tablet? Where do I go from here?

Have you tried dropping the slate (that's what it's called) on the ground? Look closely, there may be a place where dropping it has a special effect.

Note: move away a bit after dropping the slate.