Log canonical pairs with boundaries containing ample divisors

Let $(X,\mathrm{\Delta })$ be a projective log canonical pair such that $\mathrm{\Delta }\ge A$ where $A\ge 0$ is an ample $\mathbb{R}$-divisor. We prove that either $(X,\mathrm{\Delta })$ has a good minimal model or a Mori fibre space. Moreover, if $X$ is $\mathbb{Q}$-factorial, then any Log Minimal Model Program on $K_X+\mathrm{\Delta }$ with scaling terminates. As an application we prove that a log Fano type variety $X$ with $\mathbb{Q}$-factorial log canonical singularities is a Mori dream space.