
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 ellipse $C: \frac{x^{2}}{a^{2}}+y^{2}=1 (a>1)$ with foci $F_1$ and $F_2$, a circle ⊙O with the origin as its center and the focal distance of the ellipse as its diameter is internally tangent to the ellipse C at point P. Calculate the area of the triangle $PF_1F_2$.

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