
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 numbers 1 to \(n^2\) are arranged in the squares of an \(n \times n\) board (one number per square). There are \(n^2 (n-1)\) pairs of numbers in the same row or column. For each such pair, take the larger number divided by the smaller. Then take the smallest such ratio and call it the minrat of the arrangement. For example, if \(n^2\) and \(n^2 - 1\) were in the same row, then the minrat would be \(\frac{n^2}{n^2 - 1}\). What is the largest possible minrat?

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