
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 circle with radius 2 rolls around the inside of a right triangle with sides 9, 12, and 15. The circle remains tangent to at least one side of the triangle at all times. Determine the total distance traveled by the center of the circle when it returns to its starting position.

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