
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 \( 5 \) units is placed on a \( 10 \times 10 \) checkerboard with each square having a side length of 1 unit so that the centers of both the disc and the checkerboard coincide. Find the number of checkerboard squares that are completely covered by the disc.

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