1. In Rt $\triangle A B C$, $\angle C=90^{\circ}, A B=1$, point $E$ is the midpoint of side $A B$, and $C D$ is the altitude on side $A B$. Then the maximum value of $(\overrightarrow{C A} \cdot \overrightarrow{C D}) \cdot(\overrightarrow{C A} \cdot \overrightarrow{C E})$ is $\qquad$ (Li Weiwei provided the problem)