
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 perpendicular diameters $AB$ and $CD$ of a circle intersect at the center $O$ of the circle. The radius of the circle is 6. Calculate the total area of two sectors formed by these diameters, where each sector subtends a central angle of $120^\circ$, and the area of the square formed by connecting the endpoints of the diameters.

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