D&D 5E - Details of how the "Reverse Gravity" spell works

I guess that yes, what you can do while clinging to the "ceiling" will depend on the exact situation, and therefore require DM interpretation. A simple ruling would be that you need to use one hand to hang on, and the other hand is free to fight or cast or whatever. (Shooting a bow requires two hands.) Movement would be handled via the climbing rules.
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