
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
An isosceles right triangle $ABP$ with legs $AB$ and $BP$ of length $3$ inches is placed inside a square $AXYZ$ with a side length of $6$ inches. The vertex $B$ is on side $AX$. The triangle is rotated clockwise around $B$, then $P$, and so on along the sides of the square until it returns to its initial position. Calculate the length of the path in inches traversed by vertex $P$.
A) $6\pi$
B) $9\pi$
C) $12\pi$
D) $15\pi$
E) $18\pi$

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