Let $\mathscr{Y}\to\mathscr{X}$ be a log resolution of $(\mathscr{X},\mathscr{X}_{s})$. By Theorem 3.2.8, the skeleton $\mathrm{Sk}(\mathscr{X})$ is a strong deformation retract of $\mathrm{Sk}(\mathscr{Y})$. By Theorem 3.1.3, $\mathrm{Sk}(\mathscr{Y})$ is a strong deformation retract of $X_{K}^{\mathrm{an}}$. ∎