1.8: Quadrilateral with a point dividing a diagonal

The diagram shows a quadrilateral $OABC$. The point $D$ lies on $OB$ such that $\overrightarrow{OD} = 2\overrightarrow{DB}$ and $\overrightarrow{AD} = m\overrightarrow{AC}$, where $m$ is a scalar quantity.
$$\overrightarrow{OA} = \mathbf{a} \qquad \overrightarrow{OB} = \mathbf{b} \qquad \overrightarrow{OC} = \mathbf{c}$$