Example 1. As shown in the figure, in $\triangle P M N$, $C, B$ are points on $P$, $P M$, respectively. The extension of $C B$ intersects the extension of $N M$ at point $A$, and $P C = A M, P N = m, A B = n$. Find $M N: B C$.

保留源文本的换行和格式，直接输出翻译结果如下：

Example 1. As shown in the figure, in $\triangle P M N$, $C, B$ are points on $P$, $P M$, respectively. The extension of $C B$ intersects the extension of $N M$ at point $A$, and $P C = A M, P N = m, A B = n$. Find $M N: B C$.
Draw $CG // NA$ intersecting $PM$ at $G$.
$$
\begin{array}{l}
\frac{CG}{MN}=\frac{PC}{PN}, \\
\left.\begin{array}{l}
\frac{AM}{CG}=\frac{AB}{BC}
\end{array}\right\} \Rightarrow \begin{array}{l}
\frac{AM}{MN}=\frac{PC}{PN} \cdot \frac{AB}{BC} \\
PC=AM, PN=m, AB=n
\end{array} \\
\Rightarrow \frac{MN}{BC}=\frac{PN}{AB}=\frac{m}{n} .
\end{array}
$$