
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
In every row of a grid  $100 \times n$  is written a permutation of the numbers  $1,2 \ldots, 100$ . In one move you can choose a row and swap two non-adjacent numbers with difference  $1$ . Find the largest possible  $n$ , such that at any moment, no matter the operations made, no two rows may have the same permutations.

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