
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
Let \\(F_1\\) and \\(F_2\\) be the left and right foci of the ellipse \\( \dfrac {x^{2}}{25}+ \dfrac {y^{2}}{16}=1\\), and \\(P\\) be a point on the ellipse. If \\(\triangle F_1F_2P\\) is a right-angled triangle, the area of this triangle is \_\_\_\_\_\_.

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