
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 $E$: $\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1(a > b > 0)$ is $\frac{\sqrt{2}}{2}$, and the line $x+y+\sqrt{3}=0$ intersects with the ellipse $E$ at only one point.

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

(II) Line $l$ is intercepted by the circle $O$: ${x^{2}}+{y^{2}}=3$ with a chord length of $3$, and intersects with the ellipse $E$ at points $A$ and $B$, $C$ is a moving point on the circle $O$, find the maximum value of the area of $\Delta ABC$.

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