Reduced Algebraic Montgomery–Yang conjecture for rational homology projective planes

Let $S$ be a rational homology $\mathbb{CP}^2$ with at most $4$ cyclic singularities, and let $S^0$ denote its smooth locus. Reduced Algebraic Montgomery–Yang conjecture. If $S^0$ is simply-connected, $S$ is rational, and $K_S$ is ample, then $|\operatorname{Sing}(S)|\leq 3$. The source presents this as a reduction of the Algebraic Montgomery–Yang conjecture, using previously known results; it remains open in the stated generality.