Let $\overrightarrow{OB}=b$ and $\overrightarrow{AB}=a$. Express in turn the following vectors through $a$, $b$, $m$ and $n$:
\[
\overrightarrow{OA},\quad\overrightarrow{OP}, \quad\overrightarrow{OQ}, \quad\overrightarrow{AC}, \quad\overrightarrow{AQ}.
\]
Then from $\triangle OAQ$ we have $\overrightarrow{OA}+ \overrightarrow{AQ}+ \overrightarrow{QO}=0$. Use the fact that
\[
\alpha a+\beta b=0\iff \alpha=0\text{ and }\beta=0
\]
since $a$ and $b$ are linearly independent.