
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
Eight congruent disks are placed on a circle $C$ of radius 1 in such a way that the eight disks cover $C$, no two of the disks overlap, and each disk is tangent to its two neighbors. Calculate the sum of the areas of the eight disks, expressed in the form $\pi(a-b\sqrt{c})$, where $a, b, c$ are positive integers and $c$ is not divisible by the square of any prime. Find the value of $a+b+c$.

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