Can Ava Achiever's ability play Hostile Takeover (a card without action/reaction speed) during a showdown, and what is the correct timing order?

Ruling: Yes, Ava Achiever can play Hostile Takeover during a showdown. Abilities that instruct you to play other cards ignore normal timing restrictions and grant permission to play cards when they tell you to.

Sequence:

• Move Ava to attack
• Showdown starts
• Ava triggers her when attacking ability
• Ava starts resolving
• Hostile Takeover is put as pending on top of the chain with the intention of playing it from the hand
• Ava finishes resolving
• You finalize Hostile Takeover, making necessary choices like targets
• Hostile Takeover resolves

Nuances:

• The card is played from hand (not as if it were Hidden), so it won't have From-Facedown restrictions
• Action and reaction speeds normally give permission to play cards at times you normally can't; effects that instruct you to play cards grant similar permission