
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
Let the parabola $C: y^{2}=2px (p > 0)$ have focus $F$ and directrix $l$. It is known that point $A$ is on the parabola $C$, point $B$ is on $l$, and $\triangle ABF$ is an equilateral triangle with side length $4$.  
$(1)$ Find the value of $p$;  
$(2)$ Is there a point $N$ on the $x$-axis such that for any line $l′$ passing through point $N$ and intersecting the parabola $C$ at points $Q$ and $R$, the value of $ \dfrac {1}{|NQ|^{2}}+ \dfrac {1}{|NR|^{2}}$ is constant? If it exists, find the coordinates of point $N$; if not, explain why.

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