
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 that the parabola $C:y^{2}=2px$ passes through the point $E\left(4,4\right)$, and the line $l:x=\sqrt{3}y+n$ intersects the parabola $C$ at points $A$ and $B$ (distinct from point $E$), then the coordinates of the focus $F$ of the parabola are ____; if point $D\left(n,0\right)$, $|AD|\cdot |DB|=64$, then $n=$ ____.

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