
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 a focal length of $2$, and point $Q( \frac{a^{2}}{ \sqrt{a^{2}-b^{2}}},0)$ on the line $l$: $x=2$.
(1) Find the standard equation of the ellipse $C$;
(2) Let $O$ be the coordinate origin, $P$ a moving point on line $l$, and $l'$ a line passing through point $P$ that is tangent to the ellipse at point $A$. Find the minimum value of the area $S$ of $\triangle POA$.

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