Does an opportunity to play actions open up after reacting to a triggered ability?

No. After reacting to a triggered ability, you do not gain an opportunity to play an Action card.

According to the rules regarding the chain (Rule 309.1 and Rule 309.1.a), if a chain exists (a "Closed State"), you are restricted to playing or activating only cards or abilities with the Reaction keyword.

Why you cannot play an Action:

1. Closed State: A triggered ability being on the chain creates a "Closed State."
2. Restriction: In a Closed State, you cannot play [Action] cards. You can only play [Reaction] cards to add to the chain or resolve existing chain items (Rule 309.1.a, Rule 813).
3. Returning to Open State: To be able to play an [Action] card, you must be in an "Open State" (where no chain exists). The chain only empties once both players pass priority consecutively.
4. Priority after Resolution: Even after a [Reaction] resolves, the game remains in a "Closed State" as long as there are other items remaining on the chain. If your reaction was the final item on the chain, the chain resolves, and then the game returns to an "Open State," at which point you may play an [Action] (RiftJudge FAQ #1787).

Summary of the sequence:

• A triggered ability is placed on the chain (State becomes Closed).
• Players may add more items to the chain, but they must have the [Reaction] keyword.
• Once all items on the chain resolve and no chain remains (State becomes Open), you then have the opportunity to play an [Action] card.