
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
We inscribe a sphere around a unit cube, and then intersect the sphere with the planes of each face of the cube. Calculate the surface areas of the segments of the sphere that are delineated by the 6 intersecting circles.

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