
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
Consider the parabola $C$: $y^{2}=2px (P > 0)$ with focus $F$ and directrix $l$. Given that point $A$ is on parabola $C$ and point $B$ is on $l$, and $\triangle ABF$ is an equilateral triangle with side length $4$.

(1) Find the value of $P$;

(2) Does there exist a point $N$ on the $x$-axis such that when a line $l'$ passes through point $N$ and intersects parabola $C$ at points $Q$ and $R$, the value of $\frac{1}{|NQ^{2}|}+\frac{1}{|NR^{2}|}$ is constant? If so, find the coordinates of point $N$. If not, explain the reason.

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