
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
Given that a tiled surface consists of $n^2$ identical blue square tiles, each measuring $s$ inches per side, and each surrounded by a yellow border $d$ inches wide, forming an overall large square pattern, and $n=30$ being observed to cover $81\%$ of the area of the entire square region, determine the ratio $\frac{d}{s}$.

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