A rectangular garden has an area of 200 square feet. The owner decides to divide the garden into two equal parts. Later, she further divides one of those parts into two equal sections and plants flowers in one of these smaller sections. If she repeats this process (halving one of the parts) two more times, what will be the area of the section where she plants flowers at the end? Let's think step by step and output the final answer within \boxed{}.
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