
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 $P$ as a point on the ellipse $\dfrac{x^2}{25}+ \dfrac{y^2}{9}=1$, with $F_1$ and $F_2$ as the ellipse's foci, and $\angle F_1PF_2 = 60^{\circ}$, find the area $S$ of the triangle $\triangle F_1PF_2$.

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