
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
Each cell of a 5x5 table is painted in one of several colors. Lada shuffled the rows of the table so that no row remained in its original place. Then Lera shuffled the columns so that no column remained in its original place. Surprisingly, the girls noticed that the resulting table was the same as the original one. What is the maximum number of different colors that can be used to paint this table?

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