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Given that $x,y,z$ satisfy the following system of equations:-

$\begin{cases} x+\frac { 1 }{ y } =\frac { 7 }{ 3 } \\ y+\frac { 1 }{ z } =4 \\ z+\frac { 1 }{ x } =1 \end{cases}$

What is the value of $xyz$?

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