
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 region, $n^2$ blue square tiles each measuring $s$ inches on each side are laid out with a border of width $d$ inches around each tile. For $n = 30$, the tiles cover $81\%$ of the total area of the square region. Calculate the ratio $\frac{d}{s}$.
A) $\frac{1}{25}$
B) $\frac{1}{20}$
C) $\frac{1}{18}$
D) $\frac{1}{15}$
E) $\frac{1}{10}$

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