
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
Vitya has a white board made of 16 cells in the shape of a $4 \times 4$ square, from which he wants to cut out 4 white three-cell corner shapes. Petya wants to prevent him from doing this by coloring some cells red. What is the minimum number of cells he needs to color? (A corner shape is shown in the picture, possibly rotated.)

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