
When tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.

[ASSESS]

[ADVANCE]

[VERIFY]

[SIMPLIFY]

[SYNTHESIZE]

[PIVOT]

[OUTPUT]

You should strictly follow the format below:

[ACTION NAME]

# Your action step 1

# Your action step 2

# Your action step 3

...

Next action: [NEXT ACTION NAME]


system
In the Cartesian coordinate system $(xOy)$, a line $l$: $y=t (t \neq 0)$ intersects the $y$-axis at point $M$ and intersects the parabola $C$: $y^{2}=2px (p > 0)$ at point $P$. The symmetric point of $M$ about $P$ is $N$, and the line segment $ON$ is extended to intersect $C$ at point $H$.
(I) Find the ratio $\frac{|OH|}{ON}$;
(II) Are there any other common points between line $MH$ and $C$ besides $H$? Explain your reasoning.

Present the answer in LaTex format: \boxed{Your answer}
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