
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 plane cuts a sphere of radius  $ 1$  into two pieces, one of which has three times the surface area of the other. What is the area of the disk that the sphere cuts out of the plane?

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