Such a system has been built already. Its input is called an EULA, and its action is a BSOD.

(Now you need to carefully study the EULA to - potentially - prove me wrong. Good luck.)

There is a simpler solution too.

It has been stated that your first machine can do "anything".
It therefore exists in a universe where "anything" is possible - its own existence makes it so.
By definition your second machine must also be possible in that universe.

There is no need to consider how it might work, or how to create it - it simply exists.

Hey - I've already told you it's a brilliant idea xD !

On the other hand, there's a good reason why you put "anything" in quotation marks - it depends on what we mean by that. If it's "anything" in the strong sense of the word, square circles are also possible, as well as 2x2=/=4 and being both dead and alive at the same time. If we narrow it down to everything that is LOGICALLY possible, we eliminate this loophole, essentially saying "it can do anything, except for things which are impossible".
Which means it can't contradict that which is logically necessary and can only manufacture the oracle device if it can exist in the first place.

I have to correct myself. Judging from the following answers, not enough people learned that. Instead I better had written:

We should have learned: A prediction should never be input to an actual experiment.

:)