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Target opponent reveals their hand. You choose up to X nonland cards from it and exile them. For each card exiled this way, search that player's graveyard, hand, and library for any number of cards with the same name as that card and exile them. Then that player shuffles.
If you don’t exile any cards from the player’s hand, you don’t search that player’s library.
Once Reap Intellect begins to resolve, no player can cast spells or activate abilities until it has completely resolved. For example, the opponent can’t cast any cards that would be exiled after their hand is revealed.
You can choose to leave cards with those names in the zone they are in. You don’t have to exile them.
