
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
Two circles with radius  $2$  and radius  $4$  have a common center at P.  Points  $A, B,$  and  $C$  on the larger circle are the vertices of an equilateral triangle.  Point  $D$  is the intersection of the smaller circle and the line segment  $PB$ . Find the square of the area of triangle  $ADC$ .

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