（1）计算：${(\pi -2)}^0-2\cos 30°-\sqrt{16}+|1-\sqrt{3}|$．

（2）解不等式组：$\left\{\begin{array}{c}3\left(x-2\right)⩽4x-5,①\\ \frac{5x-2}{4}<1+\frac{1}{2}x\cdot ②\end{array}\right.$