
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 square plot measuring 14 by 14 cells needs to be paved with rectangular tiles sized 1 by 4. The tiles can only be laid along the grid (not diagonally), and tiles cannot be broken. What is the maximum number of tiles required? Will there be any unpaved area left?

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