A regular pentagon with area \(\sqrt{5}+1\) is printed on paper and cut out. The five vertices of the pentagon are folded into the center of the pentagon, creating a smaller pentagon. What is the area of the new pentagon? The original answer is in the form of \(n - \sqrt{m}\). Please find the value of m + n.

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