已知正方形 $\mathit{ABCD}$的边长为2，点P满足 $\overrightarrow{\mathit{AP}}=\frac{1}{2}(\overrightarrow{\mathit{AB}}+\overrightarrow{\mathit{AC}})$，则 $\left|\overrightarrow{\mathit{PD}}\right|=$_________； $\overrightarrow{\mathit{PB}}\cdot \overrightarrow{\mathit{PD}}=$_________．