
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 a \(5 \times 5\) table, all the numbers from 1 to 25 are written, one number in each cell. We consider all pairs of numbers that are in the same row or the same column. For each pair, the ratio of the larger number to the smaller number is calculated. Let \(A\) denote the minimum of these ratios among all pairs. What is the maximum possible value of \(A\) for different arrangements of the numbers in the table?

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