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Let a,b,c,d be real numbers which satisfy \frac{1}{2}\leq a,b,c,d\leq 2 and abcd=1. Find the maximum value of \left(a+\frac{1}{b}\right)\left(b+\frac{1}{c}\right)\left(c+\frac{1}{d}\right)\left(d+\frac{1}{a}\right)\text{.}

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