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If an ability would produce one or more mana of an undefined type, it produces no mana instead.

Some abilities produce mana based on the type of mana another permanent or permanents “could produce.” The type of mana a permanent could produce at any time includes any type of mana that an ability of that permanent would produce if the ability were to resolve at that time, taking into account any applicable replacement effects in any possible order. Ignore whether any costs of the ability could or could not be paid. If that permanent wouldn’t produce any mana under these conditions, or no type of mana can be defined this way, there’s no type of mana it could produce.

To “tap [a permanent] for mana” is to activate a mana ability of that permanent that includes the {T} symbol in its activation cost. See rule 605, “Mana Abilities.”

An ability that triggers whenever a permanent “is tapped for mana” or is tapped for mana of a specified type triggers whenever such a mana ability resolves and produces mana or the specified type of mana.

A replacement effect that applies if a permanent “is tapped for mana” or tapped for mana of a specific type and/or amount modifies the mana production event while such an ability is resolving and producing mana or the specified type and/or amount of mana.

If an object’s enters-the-battlefield triggered ability or replacement effect refers to X, and the spell that became that object as it resolved had a value of X chosen for any of its costs, the value of X for that ability is the same as the value of X for that spell, although the value of X for that permanent is 0. This is an exception to rule 107.3i.

The tap symbol is {T}. The tap symbol in an activation cost means “Tap this permanent.” A permanent that’s already tapped can’t be tapped again to pay the cost. A creature’s activated ability with the tap symbol in its activation cost can’t be activated unless the creature has been under its controller’s control continuously since their most recent turn began. See rule 302.6.

The untap symbol is {Q}. The untap symbol in an activation cost means “Untap this permanent.” A permanent that’s already untapped can’t be untapped again to pay the cost. A creature’s activated ability with the untap symbol in its activation cost can’t be activated unless the creature has been under its controller’s control continuously since their most recent turn began. See rule 302.6.

If you somehow exile multiple creature cards with the same Assimilation Aegis (probably because its first ability was copied or something caused it to trigger more than once), you choose one of the exiled creature cards each time its second triggered ability resolves. You don't have to choose the same one each time.

When Assimilation Aegis's second ability resolves, the creature Assimilation Aegis is attached to copies exactly what was printed on the original creature card and nothing else. It doesn't copy any information about the object the card was before it was exiled.

When the creature Assimilation Aegis is attached to becomes a copy of an exiled creature card, it's neither entering nor leaving the battlefield. Any enters-the-battlefield or leaves-the-battlefield abilities won't trigger.

If Assimilation Aegis leaves the battlefield before its first ability resolves, the target creature won't be exiled at all.

Any non-copy effects that applied to the creature Assimilation Aegis is attached to before it becomes a copy of another card will continue to apply once it becomes a copy. The same is true of any counters that are on that creature.

If there are no creature cards exiled with Assimilation Aegis when its second ability resolves, the creature Assimilation Aegis is attached to won't become a copy of anything else. It will remain just as it was.

If you somehow exile a noncreature card with Assimilation Aegis's first ability (possibly because it was a copy of a creature while on the battlefield), you can't choose to have the creature Assimilation Aegis is attached to become a copy of that card when Assimilation Aegis's second ability resolves.