
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 each cell of an \( n \times n \) table, an integer is written. It turned out that for all \( k \) from 1 to \( n \), the sum of the numbers in the \( k \)-th column is either one less or two more than the sum of the numbers in the \( k \)-th row. For which \( n \) is this possible?

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