
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 the quadrilateral pyramid \( P-ABCD \), \( BC \parallel AD \), \( AD \perp AB \), \( AB=2\sqrt{3} \), \( AD=6 \), \( BC=4 \), \( PA = PB = PD = 4\sqrt{3} \). Find the surface area of the circumscribed sphere of the triangular pyramid \( P-BCD \).

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