
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 decorative pattern covers a large floor using a \(9 \times 9\) tiling system where each \(9 \times 9\) tile set repeats consistently throughout. If each corner of the floor looks similar and symmetrical, and within each corner's \(4 \times 4\) segment of the \(9 \times 9\) set, a diagonal from one corner to the opposite is made of darker tiles (resulting in 4 darker tiles per diagonal in each \(4 \times 4\) section), what fraction of the tiles in the entire floor are darker tiles?
A) \(\frac{16}{81}\)
B) \(\frac{4}{9}\)
C) \(\frac{1}{2}\)
D) \(\frac{5}{9}\)
E) \(\frac{5}{8}\)

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