If the president has a remote way to launch nukes, that implies the existence of a broadcast signal that can be received. The signal can be emulated. Perhaps ASI helps a kid develop a science fair project dealing with radio waves. The ASI provides instructions to follow. Kid pushes button.

It doesn’t matter if this specific idea has flaws. The ASI will have lots more and plenty of patience to try them out.

Maybe it lies about a vaccines effectiveness. Maybe it’s not really a vaccine.

Maybe it cheats at an election and gets someone hired that will likely unknowingly help the ASI.

Maybe it strings together a thousand ideas that all look safe taken one by one, but cause effects that interact to cause massive problems.

You can’t imagine what it’s capable of. You simply aren’t smart enough. No one is.