
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
We color some unit squares in a  $ 99\times 99 $  square grid  with one of  $ 5 $  given distinct colors, such that each color appears  the same number of times. On each row and on each column there are no differently colored unit squares. Find the maximum possible number of colored unit squares.

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