
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
Let \( m \) be a positive integer. In a \( 4m \times 4m \) grid, two cells are called "related" if they are in the same row or the same column. Each cell is not related to itself. We color some cells in the grid blue such that each cell is related to at least two blue cells. Find the minimum number of blue cells.

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