
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 $E$: $\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$ ($a > b > 0$), the two foci of the ellipse and one endpoint of the minor axis form the vertices of an equilateral triangle. The length of the major axis is 4.

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

(II) If $A$ is the left vertex of ellipse $E$, and a line $l$ passing through the left focus $F$ intersects ellipse $E$ at points $C$ and $D$, find the maximum absolute value of the difference between the areas of $\triangle OAD$ and $\triangle OAC$. ($O$ is the origin of the coordinate system.)

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