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1. Congruences with non-coprime moduli ●○○○○ 10 ptsFind the smallest positive integer $x$ such that $x \equiv 3 \pmod{4}$ and $x \equiv 1 \pmod{6}$.
2. Solving a four-congruence CRT system ●●●○○ 50 ptsFind the least nonnegative integer $x$ satisfying $x \equiv 4 \pmod{5}$, $x \equiv 2 \pmod{7}$, $x \equiv 2 \pmod{11}$ and $x \equiv 12 \pmod{13}$.