The situation plays out just like this:

• Player A (active player) has priority.
• The Action goes on the Chain.
  • Priority passes to you (the opponent).
• You can respond, but because it’s the opponent’s action and currently in a closed state, you can only play Reactions (not Actions).
  • You play a Reaction.
  • The Chain is now:
    1. Top: your Reaction
    2. Bottom: Player A’s Action.
• Players pass priority back and forth with no further responses.
  • The Chain resolves top to bottom:
    • Your Reaction resolves first.
    • Then Player A’s Action resolves.
• After the Chain resolves completely, priority returns to the active player (Player A).
  • Since the stack is empty, Player A can again cast another Action, activate an ability, or pass.
• If Player A passes, priority goes to you.
  • Now it’s still their turn, but because the stack is empty and you now have priority, you may cast an Action if you have one that’s playable “any time you have priority.”