
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
A circular disc with diameter \(5D\) is placed on a \(10 \times 10\) checkerboard such that the centers coincide, where the side of each square on the checkerboard is \(D\). Determine the number of checkerboard squares which are completely covered by the disc.
A) 24
B) 32
C) 40
D) 48
E) 56

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