
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
What is the area of the triangle whose vertices are the points of intersection of the curves \(x^2 + y^2 = 16\) and \((x-2)^2 + 4y^2 = 36\)?
A) \( \frac{13\sqrt{80}}{9} \)
B) \( \frac{15\sqrt{80}}{9} \)
C) \( \frac{16\sqrt{80}}{9} \)
D) \( \frac{17\sqrt{80}}{9} \)
E) \( \frac{18\sqrt{80}}{9} \)

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