Neither of these assertions are true. First, the President does have authority to take military action on his own authority, which is why he can make use of nuclear weapons. The present bound is that the President cannot maintain troops abroad for longer than two months without a Congressional approval.

Secondly, the President certainly does not have unlimited power absent Congressional approval. The Trump administration imposed sanctions on ICC officials using Congressionally-granted authority (albeit under a different act, the International Emergency Economic Powers Act). That grant of authority was required to do so.