Reid's base point free conjecture for weak log Fano pairs

Let $X$ be a projective algebraic variety of dimension at least $2$ over $\mathbb{C}$, and let $D$ be a $\mathbb{Q}$-boundary such that $(X,D)$ is log canonical and $-(K_X+D)$ is nef and big.

Reid's base point free conjecture. The linear system

$$|-n(K_X+D)|$$

is free for $n\gg 0$.

This is a base point freeness assertion for weak log Fano pairs. The paper proves the claim for a special class of three-dimensional pairs, while the general statement in the stated setting is the conjectural part.