9. Given a regular quadrilateral pyramid $S-A B C D$ with lateral edge length $4, \angle A S B=30^{\circ}$, a section is made through point $A$ intersecting the lateral edges $S B, S C, S D$ at points $E, F, G$ respectively, then the minimum perimeter of the section $A E F G$ is $\qquad$
As shown in the figure, remove the base $A B C D$ of the regular quadrilateral pyramid, and unfold the side faces of the regular quadrilateral pyramid with $S A$ as one side. At this point, the four triangular side faces form an isosceles triangle $\triangle S A A^{\prime}$ with a vertex angle of $120^{\circ}$. Then, $A A^{\prime}=4 \sqrt{3}$ is the minimum value of the perimeter of the section $A E F G$.