Instant
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You perform the actions stated on a card in sequence. For some spells and abilities, you'll surveil last. For others, you'll surveil and then perform other actions.
When you surveil, you may put all the cards you look at back on top of your library, you may put all of those cards into your graveyard, or you may put some of those cards on top and the rest of them into your graveyard.
The instant or sorcery card you choose may be one that you just surveilled into your graveyard.
Mission Briefing doesn't change when you can cast the chosen card. For example, if you choose a sorcery card, you can cast it only during your main phase when the stack is empty.
Mission Briefing is still on the stack while you choose an instant or sorcery card in your graveyard. Your Mission Briefing can't be to give yourself that same Mission Briefing.
If you cast a spell this way and that card is exiled, it's considered a new object in the zone it's put into. It won't be exiled if it's put into your graveyard later in the turn.