
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 an ellipse $C: \frac{x^{2}}{a^{2}}+ \frac{y^{2}}{b^{2}}=1(a>b>0)$ with an eccentricity $e= \frac{\sqrt{3}}{2}$, and a point $M( \sqrt{3}, \frac{1}{2})$ on the ellipse.
(1) Find the standard equation of the ellipse $C$;
(2) A moving straight line $l$ (with an existing slope) intersects the ellipse at points $P$ and $Q$, and the area of $\triangle OPQ$ is $S_{\triangle OPQ}=1$. Let $N$ be the midpoint of segment $PQ$. $N_{0}$ is the projection of point $N$ on the $x$-axis. Determine if there exist two fixed points $A_{1}$, $A_{2}$ on the $x$-axis such that $\frac{|NN_{0}|^{2}}{|N_{0}A_{1}|\cdot |N_{0}A_{2}|}$ is a constant value. If they exist, find their coordinates; otherwise, explain the reason.

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