
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
The table has 25 columns and 300 rows, and Kostya painted all its cells in three colors. Then Lesha, looking at the table, for each row names one of the three colors and marks all the cells of that color in that row. (If there are no cells of the named color in the row, he marks nothing in that row.) After this, all columns containing at least one marked cell are crossed out from the table. Kostya wants to leave as few columns as possible, while Lesha wants to leave as many as possible. What is the maximum number of columns Lesha can guarantee to leave?

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