9. Given a regular quadrilateral pyramid $\mathrm{S}-\mathrm{ABCD}$ with side length of the lateral edges being $4$, and $\angle \mathrm{ASB}=30^{\circ}$, a plane is drawn through point $\mathrm{A}$ intersecting the lateral edges $\mathrm{SB}$, $\mathrm{SC}$, and $\mathrm{SD}$ at points $\mathrm{E}$, $\mathrm{F}$, and $\mathrm{G}$, respectively. The minimum perimeter of the section $\mathrm{AEFG}$ is $\qquad$
9. $4 \sqrt{3}$