
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 consisting of 16 cells forming a $4 \times 4$ square, from which he wants to cut out 4 white three-cell corners. Petya wants to prevent him by painting some cells red. What is the minimum number of cells Petya needs to paint red? (A corner is a shape, as shown in the picture, possibly rotated.)

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