
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
From a paper square of size $8 \times 8$, $n$ seven-cell corners were clipped. It turned out that it is no longer possible to clip more such corners. What is the smallest $n$ for which this is possible? A seven-cell corner is obtained by clipping a $3 \times 3$ square from a $4 \times 4$ square (by cells).

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