
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
Square $LMNO$ with side length $6$ inches contains an equilateral triangle $QRS$ with side $QR$ of length $3$ inches. $R$ is on side $LM$ of the square. The triangle is rotated counterclockwise about $R$, then $S$, and so on along the sides of the square until $S$ returns to its original position. The length of the path in inches traversed by vertex $S$ is equal to
A) $18\pi$
B) $20\pi$
C) $24\pi$
D) $30\pi$
E) $36\pi$

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