
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: $\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1 (a > b > 0)$ intersects with two parallel lines $l_1$: $y=x+b$ and $l_2$: $y=x-b$ at four points A, B, D, C, and the area of quadrilateral ABCD is $\frac{8b^2}{3}$, find the eccentricity of ellipse E.

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