
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 large square park, there are $n^2$ white square fountains, each side measuring $s$ meters. A walkway $d$ meters wide surrounds each fountain. When $n=10$, these $100$ fountains cover $40\%$ of the total area of the square park, find the ratio $\frac{d}{s}$.

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