
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
Ten congruent disks are placed on a circle $C'$ of radius $2$ so that they completely cover $C'$, with no overlaps, and each disk is tangent to its two neighbors. We need to find the sum of the areas of these ten disks.

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