Determine the number of integers $x$ such that $0\le x< 12$ and $x$ satisfies the following system of equations: \begin{align*}
&x-1\equiv 1-x\pmod {12},\\
&x-2\equiv 2-x\pmod{12}.
\end{align*}

Let's think step by step and output the final answer within \boxed{}.
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