
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
Inside a circle with radius  $6$  lie four smaller circles with centres  $A,B,C$  and  $D$ . The circles touch each other as shown. The point where the circles with centres  $A$  and  $C$  touch each other is the centre of the big circle. Calculate the area of quadrilateral  $ABCD$ .
![Image](https://1.bp.blogspot.com/-FFsiOOdcjao/XzT_oJYuQAI/AAAAAAAAMVk/PpyUNpDBeEIESMsiElbexKOFMoCXRVaZwCLcBGAsYHQ/s0/2012%2BMohr%2Bp1.png)

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