
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 radius equal to the length of 1.5 squares is placed off-center on an $8\times 8$ checkerboard such that the center of the disc is located at the center of the square in the third row and third column (counting from the top left corner). Calculate 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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