
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 eccentricity of the ellipse $C:\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1 (a > b > 0)$ is $\frac{1}{2}$, and point $M(\sqrt{3},\frac{\sqrt{3}}{2})$ is on ellipse $C$.

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

(II) If line $l$, which does not pass through the origin $O$, intersects ellipse $C$ at points $A$ and $B$, and intersects line $OM$ at point $N$, with $N$ being the midpoint of segment $AB$, find the maximum area of $\triangle OAB$.

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