
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 a square section of a tiled floor, with a repeating pattern that expands across the entire floor and is symmetrical at all four corners, the tiling pattern repeats every $4 \times 4$ tiles, and a quarter-section of this pattern contains 3 dark tiles, calculate the fraction of the entire floor made of darker tiles.

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