
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 are making a "dice" from a spherical body by cutting off six identical spherical caps so that the circular disks formed at the places of the spherical caps each touch four neighbors. What percentage of the total area of these six circular disks is of the total surface area of the dice?

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