
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 the parabola $E$: $y^2=2px$ ($p > 0$) and a point $M$ $(x\_0, 4)$ on it, the distance between $M$ and the focus $F$ is $|MF|= \frac{5}{4} x\_0$.
(I) Find the equation of the parabola $E$;
(II) A line $l$ passes through $F$ and intersects $E$ at points $A$ and $B$. The perpendicular bisector of $AB$, denoted as $l'$, intersects $E$ at points $C$ and $D$. If $\overrightarrow{AC} \cdot \overrightarrow{AD} =0$, find the equation of line $l$.

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