A company decides to offer a special discount on its new product. The price of the product is defined by the function $P(x) = 100 \times (0.9)^x$, where $x$ represents the number of months since the product was launched. If the company also offers a flat discount of $20$ after 6 months, what will be the cost of the product after 6 months? Let's think step by step and output the final answer within \boxed{}.
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