What is the volume of the region in three-dimensional space defined by the inequalities $|x|+|y|+|z|\leq 1$ and $|x|+|y|+|z-1|\leq 1$ ?

$\frac{1}{2}$
1
$\frac{1}{3}$
$\frac{1}{6}$
$\frac{2}{3}$

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