
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
Given a $100 \times 100$ grid where cells are colored black and white, every column has an equal number of black cells, while every row has a different number of black cells. What is the maximum possible number of pairs of adjacent cells (sharing a common side) that are of different colors?

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