
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 garden, $n^2$ white square tiles, each of side $s$ meters, are symmetrically laid. A uniform border $d$ meters wide surrounds each tile. When $n=30$, these $900$ white tiles cover $81\%$ of the total area of the garden. Determine the ratio $\frac{d}{s}$ for this arrangement.
- **A)** $\frac{1}{20}$
- **B)** $\frac{1}{18}$
- **C)** $\frac{1}{16}$
- **D)** $\frac{1}{14}$
- **E)** $\frac{1}{12}$

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