It's OK to omit the "to" in the first. In the second, "to" cannot be added, since "countries take the action" is a clause, and "take" is the verb.. making sure (that) other countries take the action that we're taking to stop this becoming worse.
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FandorinThe sentence is perhaps acceptable without to before take, in which case take begins a that-clause even though
But we need other countries to work with us and that's what I'm also spending my time making sure other countries (to)
take the action that we're taking to stop this becoming worse.