
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
Consider a large, square floor fully covered with tiles in a repeating pattern. Each \(4 \times 4\) section of tiling contains a \(2 \times 2\) block at the top left corner where 3 of these tiles are dark, and the rest of the \(4 \times 4\) section contains only 2 more dark tiles. If each corner of the floor exhibits this same configuration, what fraction of the tiles on the floor are dark?

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