
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 the equations of the two asymptotes of a hyperbola are $3x \pm 4y = 0$, and point $A$ is on the right branch of the hyperbola, while $F_1(-5, 0)$ and $F_2(5, 0)$ are the left and right foci of the hyperbola, respectively. If $\angle{F_1AF_2} = 60^{\circ}$, calculate the area of $\triangle{F_1AF_2}$.

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