
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
Let  $n$  be a positive integer. Find the greatest possible integer  $m$ , in terms of  $n$ , with the following property: a table with  $m$  rows and  $n$  columns can be filled with real numbers in such a manner that for any two different rows  $\left[ {{a_1},{a_2},\ldots,{a_n}}\right]$  and  $\left[ {{b_1},{b_2},\ldots,{b_n}} \right]$  the following holds: \[\max\left( {\left| {{a_1} - {b_1}} \right|,\left| {{a_2} - {b_2}} \right|,...,\left| {{a_n} - {b_n}} \right|} \right) = 1\]
*Poland (Tomasz Kobos)*

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