
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 \( m \) rows and \( n \) columns. A horizontal move is defined as a permutation of the elements in the table such that each element stays in the row it was in before the permutation; similarly, a vertical move is defined as a permutation where "row" in the previous definition is replaced by "column". Determine \( k \) such that in \( k \) moves (any combination) any permutation of the table elements can be obtained, but there exists such a permutation that cannot be obtained in fewer moves.

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