Actually, when you link up 2 neural networks, or even a neural network and, say, a search algorithm, the neural network rapidly learns to use the external algorithm to do what it was planning to do anyway.

So there is no "beating" a neural network. The reward for having such a search algorithm is simply the ability to put thoughts into your mind. Your mind may still reject them, and if you don't feed it enough relevant data, it will rapidly abandon you.