
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 foci of the ellipse $\frac{x^2}{100} + \frac{y^2}{64} = 1$, and point $P$ is on the ellipse. If $\angle F\_1 P F\_2 = \frac{\pi}{3}$, find the area of $\triangle F\_1 P F\_2$.

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