
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
 $A, B, C$ , and  $D$  are all on a circle, and  $ABCD$  is a convex quadrilateral. If  $AB = 13$ ,  $BC = 13$ ,  $CD = 37$ , and  $AD = 47$ , what is the area of  $ABCD$ ?

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