
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 corner of a tiled floor is shown. If the entire floor is tiled in this way and each of the four corners looks like this one, determine the fraction of the tiled floor that is made of darker tiles, considering that the repeating pattern is a $4 \times 4$ grid and the top $2 \times 2$ area contains 3 dark tiles.

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