A right square pyramid has its apex directly above the center of its square base. A plane parallel to the base cuts the pyramid, creating a smaller, similar square pyramid. The area of the base of the smaller pyramid is 64 square feet, and the area of the base of the original pyramid is 256 square feet. If the height of the original pyramid is 12 feet, how far above the base is the smaller pyramid's base? Let's think step by step and output the final answer within \boxed{}.
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