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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.

A spell you cast this way can be the target of a later spell you cast this way. However, permanent spells cast this way won’t resolve until you’re done casting spells, so the permanents they become can’t be the target of spells cast this way. For example, if you exile Twincast and Lightning Strike, you can cast Lightning Strike and then cast Twincast targeting it; but if you exile a creature card and an Aura card, you can’t cast that Aura targeting that creature.

If you cast a spell “without paying its mana cost,” you can’t pay any alternative costs. You can, however, pay additional costs. If the spell has any mandatory additional costs, those must be paid to cast it.

For chapter I of The Great Synthesis, the number of cards you draw is determined as the ability resolves. If you no longer control The Great Synthesis at that time, your maximum hand size remains unchanged.

If a spell has {X} in its mana cost, you must choose 0 as the value of X when casting it without paying its mana cost.

Once you’ve activated Jin-Gitaxias’s last ability, it doesn’t matter what happens to the number of cards in your hand. The ability will resolve even if you have six or fewer cards in your hand by that time.

All the spells you cast due to chapter III are cast during the resolution of that ability. You can cast them in any order, and timing restrictions based on the cards’ types are ignored. Once you’re done casting spells, before any of them resolve, The Great Synthesis will be exiled and return as Jin-Gitaxias.