Solve the system of congruences to find the smallest positive integer \( x \):

\[
\begin{cases}
x \equiv 2 \pmod{3} \\
x \equiv 3 \pmod{5} \\
x \equiv 1 \pmod{7}
\end{cases}
\] Let's think step by step and output the final answer within \boxed{}.
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