
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 $\triangle ABC$, $\angle C = 90^{\circ}$ and $AB = 15$. A rectangle $ABXY$ with $\angle BAX = 90^{\circ}$ and $AX = 2AB$, and a square $BCWZ$ are constructed outside of the triangle. Points $X, Y, Z$, and $W$ all lie on a circle. What is the perimeter of $\triangle ABC$?
A) $30 + 15\sqrt{2}$
B) $30$
C) $15 + 15\sqrt{2}$
D) $22.5$
E) $37.5$

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