
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 $\triangle ABC$, $\angle C = 90^\circ$, $\triangle ABC$ is isosceles with $AB = 10$. Squares $ABXY$ and $CBWZ$ are constructed outside of the triangle. Points $X$, $Y$, $Z$, and $W$ lie on a circle. What is the perimeter and area of the triangle?
**A)** $10+5\sqrt{2}, 20$  
**B)** $10+10\sqrt{2}, 25$  
**C)** $15+5\sqrt{2}, 30$  
**D)** $20+10\sqrt{2}, 35$  
**E)** $10+10\sqrt{2}, 30$

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