
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
The foci of the ellipse $\dfrac{x^2}{25} + \dfrac{y^2}{9} = 1$ are $F_1$ and $F_2$, and $P$ is a point on the ellipse. It is known that $PF_1 \perp PF_2$. Then, the area of $\triangle F_1PF_2$ is ______.

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