
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 $\sqrt{2}$ units is placed so that its center coincides with the center of a square of side $1$ unit within an $8 \times 8$ checkerboard. Each square on the checkerboard has dimensions $1 \times 1$ unit. How many squares of the checkerboard are completely covered by the disc?
A) 0
B) 1
C) 2
D) 4
E) More than 4

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