
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 ${F_1}$ and ${F_2}$ are the two foci of the ellipse $\frac{x^2}{9} + \frac{y^2}{7} = 1$, and $A$ is a point on the ellipse such that $\angle AF_1F_2 = 45^\circ$, find the area of $\Delta AF_1F_2$.

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