
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  $7\times7$  table is painted with one of several colours. It is known that for any two distinct rows the numbers of colours used to paint them are distinct and for any two distinct columns the numbers of colours used to paint them are distinct.What is the maximum possible number of colours in the table?

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