
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
In the Cartesian coordinate system, for the ellipse C: $$\frac {x^{2}}{25} + \frac {y^{2}}{9} = 1$$, the left and right foci are denoted as F<sub>1</sub> and F<sub>2</sub>, respectively. Let P be a point on the ellipse C such that line segments PF<sub>1</sub> and PF<sub>2</sub> are perpendicular to each other. Find the area of triangle △PF<sub>1</sub>F<sub>2</sub>.

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