
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
Three identical circles touch one another, with each circle's circumference being 30. What is the perimeter of the triangular shaded region formed where all three circles touch? Each shaded arc corresponds to the area between the touch points of each circle with its adjacent circles.

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