Attacks » Assembly GX | Trainers » Beast Ball
Does using Beast Ball count as "taking a prize" for the purpose of calculating damage for Stakataka GX's "Assembly GX" attack?
No, it does not. You are switching cards, not taking a prize.
Source: TPCi Rules Team (2018-08-16)

Relevant cards

Note: All applicable cards may not be listed below.
SM7_102
SM7_125
SM7_159
SM7_176
SMA_SV74
SMA_SV74