10. Point $P\left(x_{0}, y_{0}\right)$ is any point on the ellipse $\frac{x^{2}}{8}+\frac{y^{2}}{2}=1$, and the line $y=k x+m(k m \neq 0)$ intersects the ellipse $C_{1}: \frac{x^{2}}{4}+y^{2}=1$ to form a chord $M N$ which is bisected by the line $O P$ and satisfies $m y_{0}>-1$. The area of $\triangle P M N$ is 1. Determine the shape of quadrilateral $O M P N$ and the number of common points between the line $P M$ and the ellipse $C_{1}$. Prove your conclusions.