Can you play an action on top of a reaction during a showdown?

No, you cannot play an Action spell on top of a Reaction spell during a showdown.

According to the rules and established gameplay mechanics:

1. Action spells require an Open State: An Action spell can only be played when the chain is empty (an "Open State").
2. Playing a Reaction creates a Closed State: When a player plays a Reaction (or any card) to start or add to a chain, the showdown enters a "Closed State."
3. Only Reactions in a Closed State: While a chain exists (Closed State), you can only play spells or abilities with the Reaction keyword. You cannot play an Action spell until the current chain has fully resolved and the state returns to Open.

Sequence:

• A chain is currently open (e.g., a player has played a Reaction). The state is Closed.
• You cannot play an Action spell because the chain is not empty.
• You may only play a Reaction spell to respond to the existing chain.
• Once the chain resolves and becomes empty, the state returns to Open.
• The player with focus may then play a new Action spell to start a new chain.

This is confirmed by RiftJudge FAQ #8963: "You cannot play an Action spell in response to an opponent's Action spell during a showdown. You can only respond with Reaction spells because Action speed cannot be played during a closed state (ongoing chain)."