I'd love to understand what you said about re-arranging terms, but I don't. Can you explain in more detail how you get from the first set of hypotheses/choices (which I understand) to the second?

I just moved the right hand side down by two spaces. The sum still stays the same, but the relative inequality flips.

As I said earlier, my solution is an argument that in every case there will be an action that strictly dominates all the others.

Why would you think that? I don't really see where you argued for that, could you point me at the part of your comments that said that?