
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
In a \(4 \times 4\) square, each of the 16 cells is colored either black or white. Then, in each of the nine \(2 \times 2\) sub-squares that can be highlighted within the given square, the number of black cells is counted. The resulting counts are 0, 2, 2, 3, 3, 4, 4, 4, 4. How many black cells can there be in the large square? List all possible options.

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