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If a,b,ca, b, c a,b,c are distinct real numbers such that a+1b=b+1c=c+1a,a+\frac{1}{b}=b+\frac{1}{c}=c+\frac{1}{a},a+b1=b+c1=c+a1, find ∣abc∣.|abc|.∣abc∣.
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