
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
Let  $ABCD$  be a cyclic quadrilateral, and  $E$  be the intersection of its diagonals. If  $m(\widehat{ADB}) = 22.5^\circ$ ,  $|BD|=6$ , and  $|AD|\cdot|CE|=|DC|\cdot|AE|$ , find the area of the quadrilateral  $ABCD$ .

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