
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
In a square chessboard composed of 8 × 8 squares with a side length of 8, a circle with a radius of 4 is placed. Let \( S_1 \) be the sum of the areas inside the circle of all the small squares through which the circle's circumference passes, and let \( S_2 \) be the sum of the areas outside the circle of all the small squares through which the circle's circumference passes, calculate the integer part of \( \frac{S_1}{S_2} \).

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