
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
Inside an equilateral triangle with side length \( a \), there are three equal circles, each touching two sides of the triangle and the other two circles. Find the area of the part of the triangle that is outside these circles.

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