
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 $(C)$: $\frac{x^{2}}{a^{2}}+ \frac{y^{2}}{b^{2}}=1 (a > b > 0)$ that passes through point $A(2,3)$ with its right focus at $F(2,0)$.
1. Find the equation of ellipse $(C)$.
2. Assume the origin as $O$, and a line $(l)$ parallel to $OA$ that intersects with ellipse $(C)$. The distance between $OA$ and $(l)$ is equal to $\sqrt{13}$. Find the equation of line $(l)$.

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