
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
Given a parabola $C$: $y^{2}=2px (p > 0)$ with focus $F$, the line $y=4$ intersects the $y$-axis at $P$ and the parabola at $Q$. Additionally, $|QF|= \frac{5}{4}|PQ|$.
(I) Find the equation of the parabola $C$;
(II) A line $l$ passing through $F$ intersects $C$ at two points $A$ and $B$. The perpendicular bisector $l'$ of segment $AB$ intersects $C$ at points $M$ and $N$. If points $A$, $M$, $B$, and $N$ lie on the same circle, find the equation of line $l$.

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