
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
Andrey placed chips of 100 different colors on a $10 \times 10$ board. Every minute, one chip changes its color, and the chip that changes color must have been unique (distinguishable by color from all others) in its row or column before the operation. After $N$ minutes, it turned out that no chip could change its color anymore. What is the minimum possible value of $N$?

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