7. In the Cartesian coordinate system, there are four fixed points $A(-3,0)$, $B(1,-1)$, $C(0,3)$, $D(-1,3)$, and a moving point $P$. Then the minimum value of $|P A|+|P B|+|P C|+|P D|$ is $\qquad$.
$$
\text { II. } 7.3 \sqrt{2}+2 \sqrt{5} \text {. }
$$

As shown in Figure 5, let $A C$ and $B D$ intersect at point $F$, then
$$
\begin{array}{l}
|P A|+|P C| \\
\geqslant|A C|=|F A|+|F C|, \\
|P B|+|P D| \\
\geqslant|B D|=|F B|+|F D| .
\end{array}
$$

Therefore, when the moving point $P$ coincides with $F$, $|P A|+|P B|+$ $|P C|+|P D|$ reaches its minimum value $|A C|+|B D|=3 \sqrt{2}+2 \sqrt{5}$.