
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
Eighteen congruent disks are placed on a circle \(C\) of radius 1 in such a way that the eighteen disks cover \(C\), no two of the disks overlap, and so that each of the eighteen disks is tangent to its two neighbors. Calculate the sum of the areas of the eighteen disks.

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