Groups acting distally and minimally on ${\mathbb{S}}^2$ and ${\mathbb{R}\mathbb{P}}^2$

Let $X$ be the $2$-sphere ${\mathbb{S}}^2$ or the real projective plane ${\mathbb{R}\mathbb{P}}^2$. We show that if $\mathrm{\Gamma }$ is a finitely generated group acting minimally and distally on $X$, then $\mathrm{\Gamma }$ contains a nonabelian free subgroup.