
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 the hyperbola $$\frac {x^{2}}{9} - \frac {y^{2}}{16} = 1$$ with its left and right foci marked as F<sub>1</sub> and F<sub>2</sub> respectively. If there is a point P on the hyperbola such that the angle ∠F<sub>1</sub>PF<sub>2</sub> is 90°, find the area of triangle ΔF<sub>1</sub>PF<sub>2</sub>, denoted as $$S_{△F_{1}PF_{2}}$$.

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