A quarry wants to sell a large pile of gravel. At full price, the gravel would sell for $3200$ dollars. During the first week, the quarry sells $60\%$ of the gravel at full price. The following week, the quarry reduces the price by $10\%$, and again, it sells $60\%$ of the remaining gravel. Each subsequent week, the quarry continues to reduce the price by another $10\%$ and sells $60\%$ of the remaining gravel. This process continues until only a handful of gravel is left. How many dollars does the quarry collect for the sale of all its gravel?

Let's think step by step and output the final answer within \boxed{}.
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