Write a self-executable Python program that leverages both a basic 2-layer Artificial Neural Network utilizing static backpropagation using Numpy and that utilizes either Best-First search, Greedy Best First search, Beam search, or A* search methods to calculate an appropriate output based on a function that sorts movie preferences. The program should be complete and straightforward to test. The submission must function and be a reasonable attempt at a solution for your chosen problem. The solution does not have to be correct or useful in the real world, but the solution MUST provide reasonable answers without error.