The top card of your library isn’t in your hand, so you can’t cycle it, discard it, or activate any of its activated abilities.

Precognition Field lets you look at the top card of your library whenever you want (with one restriction—see below), even if you don’t have priority. This action doesn’t use the stack. Knowing what that card is becomes part of the information you have access to, just like you can look at the cards in your hand.

If the top card of your library changes while you’re casting a spell, playing a land, or activating an ability, you can’t look at the new top card until you finish doing so. This means that if you cast the top card of your library, you can’t look at the next one until you’re done paying for that spell.

You must follow the normal timing permissions and restrictions of the cards you play from your library.

You’ll still pay all costs for that spell, including additional costs. You may also pay alternative costs such as that granted by Jodah, Archmage Eternal.

The card you’ll exile from the top of your library is determined as Precognition Field’s last ability resolves. This might not be the card that was on top of your library when you activated that ability.