Can you use an action spell on an action spell during a showdown?

No, you cannot play an Action spell in response to an Action 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 an Action spell creates a Closed State: When a player plays an Action spell, it starts a chain. This puts the showdown into 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:

• Player A plays an Action spell (starts a chain, state becomes Closed).
• Player B cannot play an Action spell because the chain is not empty.
• Player B may play a Reaction spell to respond to Player A's spell.
• 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 FAQ #6353: "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)."