I think you can. As long as everything is zipped up and you don't have anything sharp that could potentially puncture the trampoline. However, I felt safe leaving my stuff in a cubby or on one of the benches near the area my kids were jumping.
I've never seen anyone Carey there's while jumping but I dont think you can't. They have little cubbies to put your things or I'll just leave certain things in my car if I don't need it
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