
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 $100 \times 100$ square grid, some cells are colored. Each colored cell is the only colored cell either in its column or in its row. What is the maximum number of cells that can be colored?

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