
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 large circular disc with a diameter of $2S$ and a small circular disc with diameter $S$ are placed on a $10\times 10$ checkerboard, with each square having a side length of $S$. The center of the large disc coincides with the center of the checkerboard. The small disc is placed so that its center is at the top left corner of the central square of the checkerboard. Find the number of checkerboard squares completely covered by at least one of the discs.

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