In the diagram, \(\overrightarrow{OA}=\mathbf a\) and \(\overrightarrow{OB}=\mathbf b\).

The point \(M\) is the midpoint of \(OB\).

The point \(N\) is such that \(\overrightarrow{ON}=3\overrightarrow{NA}\).

The lines \(BN\) and \(AM\) intersect at the point \(X\).

\(\overrightarrow{BX}=\lambda\overrightarrow{BN}\), where \(\lambda\) is a constant.

\(\overrightarrow{MX}=\mu\overrightarrow{MA}\), where \(\mu\) is a constant.

(a) Find \(\overrightarrow{OX}\) in terms of \(\mathbf a\), \(\mathbf b\) and \(\lambda\).

(b) Find \(\overrightarrow{OX}\) in terms of \(\mathbf a\), \(\mathbf b\) and \(\mu\).

(c) Hence find the values of \(\lambda\) and \(\mu\).