Photoshop Elements has an action player. However, you can only produce the action in full Photoshop. If you use xyz (hypothetical) tool in full Photoshop, it will not play in PSE because PSE does not have xyz tool. PSE is a low cost consumer product.
I have absolutely no experience writing actions, but I have downloaded & installed actions and played them in PSE.
The above referenced link provides more information.
Check with someone in your community with Photoshop - - there must be a guru!
Also, click on this link and under "Search" enter actions. The moderator of that forum is named Sepiana and she is very conversant with actions.