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If a,b,\color{#3D99F6}{a},\color{#D61F06}{b},a,b, and c\color{#20A900}{c}c are distinct reals such that a+1b=b+1c=c+1a,\color{#3D99F6}{a}+\dfrac {1}{\color{#D61F06}{b}}=\color{#D61F06}{b}+\dfrac {1}{\color{#20A900}{c}}=\color{#20A900}{c}+\dfrac {1}{\color{#3D99F6}{a}},a+b1=b+c1=c+a1, then find the value of ∣abc∣.|\color{#3D99F6}{a}\color{#D61F06}{b}\color{#20A900}{c}|.∣abc∣.
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