
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 disk with a diameter of \( D \) is placed on a chessboard with an \( 8 \times 8 \) grid, where the width of each square is \( D \), and their centers coincide. Find the number of squares on the chessboard that are completely covered by the disk.

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