
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
In an equilateral triangle, three circles are inscribed such that each circle touches two sides of the triangle and the other two circles. Each circle has a radius of 2, and there is an offset of 1 unit from each vertex to the nearest point on any circle. Calculate the perimeter of this equilateral triangle.
A) $6\sqrt{3} + 12$
B) $9\sqrt{3} + 18$
C) $18\sqrt{3} + 6$
D) $12\sqrt{3} + 10$

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