
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
A set of (unit) squares of a  $n\times n$  table is called *convenient* if each row and each column of the table contains at least two squares belonging to the set. For each  $n\geq 5$  determine the maximum  $m$  for which there exists a *convenient* set made of  $m$  squares, which becomes in*convenient* when any of its squares is removed.

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