The Free Peoples player chooses. The text says "to make the Free Peoples player" and even though it's stated only before the exertion part, it refers to the discarding part of the text as well.
As for the linguistic side: I'm not quite sure about English language, but in my language it'd be called redundancy if the text said: "to make the Free Peoples player" on both exertion and discarding part of the text (hope this makes sense

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