
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 semicircle is constructed on the base of an equilateral triangle as its diameter, and this semicircle divides the triangle into two parts. The side of the triangle is \(a\). Find the area of the part of the triangle that lies outside the semicircle.

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