3.37: Parallelogram vector ratio

In parallelogram $OABC$, $D$ divides $OC$ in the ratio $2:3$, $\overrightarrow{OA}=\mathbf{a}$, $\overrightarrow{OC}=\mathbf{c}$. Point $P$ on $AD$ satisfies $\overrightarrow{OP}=m\overrightarrow{OB}$ and $\overrightarrow{AP}=n\overrightarrow{AD}$.

Find two expressions for $\overrightarrow{OP}$ and hence find integers $m$ and $n$.