Polarized endomorphisms of Fano varieties with complements

Let $X$ be a Fano type variety and $(X,\mathrm{\Delta })$ be a log Calabi-Yau pair with $\mathrm{\Delta }$ a Weil divisor. If $(X,\mathrm{\Delta })$ admits a polarized endomorphism, then we show that $(X,\mathrm{\Delta })$ is a finite quotient of a toric pair. Along the way, we prove that a klt Calabi-Yau pair $(X,\mathrm{\Delta })$ with standard coefficients that admits a polarized endomorphism is the quotient of an abelian variety.