SEAMO 2027 - Paper E - SET 06 - Self-study Question 13

In square $ABCD$, the diagonals intersect at $O$. Ray $AF$ bisects $\angle BAC$, meeting $BD$ at $G$ and $BC$ at $F$. Given $OG:CF=m:n$, where $m,n$ are coprime positive integers, find $m+n$.