
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 with the equation $\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1 (a > b > 0)$ and an eccentricity of $e = \frac{\sqrt{2}}{3}$, the focal length is $2\sqrt{2}$.

(1) Find the equation of the ellipse.

(2) Point $A$ is a point on the ellipse, and ${F_1}, {F_2}$ are the two foci of the ellipse. If $\angle {F_1}A{F_2} = {60^0}$, find the area of $\Delta A{F_1}{F_2}$.

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