
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
A plane contains an equilateral triangle and three circles centered at its vertices, with the radius of each circle being less than the height of the triangle. A point on the plane is colored yellow if it lies inside exactly one of the circles, green if it lies inside exactly two, and blue if it lies inside all three circles. It is given that the yellow area is 1000, the green area is 100, and the blue area is 1. Find the area of the triangle. (P. D. Mulenko)

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