
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 of $\frac{\sqrt{3}}{2}$, the distance from its right focus $F$ to the line $x-y+\sqrt{3}=0$ is $\sqrt{6}$.
(I) Find the standard equation of the ellipse $C$;
(II) A line passes through the right focus $F$ of the ellipse $C$ with an inclination angle of $45^{\circ}$ and intersects $C$ at points $M$ and $N$. Find the area of triangle $OMN$ ($O$ is the origin).

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