The clue to the puzzle is hidden somewhere within Summer Shepherd City.
Just like the city's power source, cracking this time loop would also require a research in this direction.
...
"We need to find the clue as soon as possible..."
"Yes. Otherwise, the time loop may trap us here forever."
"..."
Leonard Churchill and his companions strolled down the streets while discussing potential strategies.
Even though they had Elder Clinton's cheat code, his amnesia was not reliable at all times.
They might have been trapped in this Mysterious Realm for more than a couple of days already.
No one dared to say there would be no dangers if they continued to be trapped.
They needed to break the loop as soon as possible.