
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 courtyard is designed with 400 smaller square tiles arranged in a 20x20 grid. Each tile measures 't' meters on a side, and each tile is surrounded by a uniform path 'p' meters wide around all sides. The combined area of the paths takes up 75% of the total area of the courtyard. Determine the ratio $\frac{p}{t}$.
A) \( \frac{1}{4} \)
B) \( \frac{1}{3} \)
C) \( \frac{1}{2} \) (0.5)
D) \( \frac{2}{3} \)

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