
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
Let  $N$  be a positive integer. Consider a  $N \times N$  array of square unit cells. Two corner cells that lie on the same longest diagonal are colored black, and the rest of the array is white. A *move* consists of choosing a row or a column and changing the color of every cell in the chosen row or column. 
What is the minimal number of additional cells that one has to color black such that, after a finite number of moves, a completely black board can be reached?

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