Can you play spells that are neither action nor reaction (like Cull the Weak) during a showdown on your turn?

Ruling: You cannot play spells that are neither action nor reaction during a showdown, even on your turn. These spells can only be played during your turn, out of showdown, when the chain is empty.

Sequence:

• Must be during your turn
• Must be out of showdown
• Must be when the chain is empty

Nuances:

• Cards with "action" timing can be played during a showdown
• Cards with "reaction" timing can be played anytime you're given priority
• Main timing spells are restricted to your main phase only