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On every evening, before attempting the tower, you should always talk to Fuuka or Mitsuru (when you have just started out). They will give you an update of all the characters' health. You wouldn't want to assult the tower's enemies when your characters look tired or sick. As their skills would drastically drop.

Teleportation Points

As with the original Persona 3. Each section of the Tartarus has a teleportation point, which lets you return to the entrance. The latter half of the teleportation point lets you return to the floor you've just completed, instead of having to start from the very beginning.