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We ended being forced to mount a giant bug. It was slightly creepy when I looked at the creature's giant jaws and eyes, but after sitting over its golden back and then beginning to move through the streets, I found the experience rather relaxing! I also found Silver, Mimy, Belle, and Loki, who had come rushing towards me the moment they felt I logged in. Summons and Tamed Pets stay in the game while you are offline, so it is usually necessary to find a place where you can leave them until you return.
This is why some serious players that usually explore the world constantly can't settle down with a house to put their summons/tamed monsters and have to go to the Market City where Players can teleport into and pay an expensive barn to leave them resting in there, which accumulates debt the more hours you leave them.