
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 table of size \( n \times n \) cells: two opposite corner cells are black, and the rest are white. What is the minimum number of white cells that need to be repainted black so that, using transformations consisting of repainting all the cells of any column or any row to the opposite color, it is possible to make all the cells in the table black?

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