
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
A large square region is paved with $n^2$ square black tiles, where each tile measures $t$ inches on each side. Surrounding each tile is a white border that is $w$ inches wide. When $n=30$, it's given that the black tiles cover $81\%$ of the area of the large square region. Find the ratio $\frac{w}{t}$ in this scenario.
A) $\frac{1}{8}$
B) $\frac{1}{9}$
C) $\frac{2}{9}$
D) $\frac{1}{10}$
E) $\frac{1}{11}$

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