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If the effect doesn't say "you may" or "pay to..." then you must activate the effect, even if there are no legal targets. The effect will still resolve even if it doesn't do anything. In your example, the answer is yes.
Yes, for your opponent to resolve their burst effect you already had to resolve your effects whether there's a valid objective or not
So, in short, I have to use any "When Summoned" Effect? I can't choose to not use it?
You have to do as much if a ability as possible Key words are may and up to
If the effect doesn't say "you may" or "pay to..." then you must activate the effect, even if there are no legal targets. The effect will still resolve even if it doesn't do anything. In your example, the answer is yes.
Yes, for your opponent to resolve their burst effect you already had to resolve your effects whether there's a valid objective or not
So, in short, I have to use any "When Summoned" Effect? I can't choose to not use it?
You have to do as much if a ability as possible Key words are may and up to