3.45: Vector geometry: lines $PQ$ and $OB$

In triangle $OAB$, $\overrightarrow{OA}=\mathbf{a}$ and $\overrightarrow{OB}=\mathbf{b}$. Point $P$ on $OA$ has $\overrightarrow{OP}=\tfrac{3}{4}\overrightarrow{OA}$. Point $Q$ on $AB$ has $\overrightarrow{AQ}=\tfrac{1}{3}\overrightarrow{AB}$. Line $PQ$ meets $OB$ at $R$ with $\overrightarrow{OR}=m\mathbf{b}$ and $\overrightarrow{PR}=n\overrightarrow{PQ}$.

Find $\overrightarrow{OR}$ in terms of $\mathbf{a}$, $\mathbf{b}$ and $n$.

Hence find the values of $m$ and $n$.