
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 circles form a ring with each circle externally tangent to the two circles adjacent to it. All eight circles are internally tangent to a circle $\cal D$ with radius 40. Let $K'$ be the area of the region inside $\cal D$ and outside all of the eight circles in the ring. Find $\lfloor K'\rfloor$.

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