The diagram shows a triangle \(OAB\). The point \(C\) is the midpoint of \(OA\). The point \(D\) lies on \(CB\) such that \(CD:DB=2:3\).

\(\overrightarrow{OC}=\mathbf c,\qquad \overrightarrow{CB}=\mathbf b.\)

The point \(E\) lies on \(AB\) such that \(\overrightarrow{OE}=\lambda\overrightarrow{OD}\) and \(\overrightarrow{AE}=\mu\overrightarrow{AB}\), where \(\lambda\) and \(\mu\) are scalars. Find two expressions for \(\overrightarrow{OE}\), each in terms of \(\mathbf b\), \(\mathbf c\) and a scalar, and hence find \(AE:EB\).