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If you control more than one Sylvan Library, the triggered ability of each will resolve in sequence. You don’t get to draw all the cards at once and then put them all back at once.
You can put back zero, one, or two cards.
You always perform your normal draw before this ability. The normal draw occurs before anything can be placed on the stack during a player’s draw step.
Any cards drawn prior to Sylvan Library’s ability resolving, including in your upkeep or in response to Sylvan Library’s triggered ability, can be chosen to be put back using this effect. Sylvan Library’s controller is responsible for keeping these cards distinguishable in hand, such as by keeping them separate from cards that began the turn in hand.
It’s not possible to take any actions between drawing the cards and choosing two cards. You can’t cast the cards you drew to avoid having two cards to choose.
If you control other triggered abilities that allow you to draw cards during your draw step, you can choose to order Sylvan Library’s ability before or after those abilities. Triggered abilities controlled by other players will resolve before triggered abilities you control.
If you choose to draw two cards, then replace one or more of those draws with some other effect, the rest of Sylvan Library’s ability still happens. If you’ve actually drawn only one card that turn, you must choose that card and either pay 4 life or put it on top of your library. If you haven’t actually drawn any cards that turn, the rest of the ability has no effect.