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Wrong, you can use both traps or both gears if so you desire. You could dump every ability card and gear/trap, so as long as the card timings are correct.
Not neccesarily the same time, you still have to ask your opponent if they want to play anything. If they decline, then you can use the next. It goes like this,P1 can use one card/sub-bakuganP2 can use one card/sub-bakuganP1 can use one card/sub-bakuganetc...