
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 that the ellipse $C$: $\frac{{x}^{2}}{{a}^{2}}+\frac{{{y}^{2}}}{{{b}^{2}}}=1(a > b > 0)$ has a minor axis length of $2\sqrt{3}$, and an eccentricity of $\frac{1}{2}$.

(I) Find the standard equation of the ellipse $C$;

(II) Let $O$ be the coordinate origin, and the line $l$ passes through the focus of the ellipse and intersects the ellipse at $M$ and $N$. Find the maximum area of $\triangle OMN$.

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