
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
For which integers  $n\ge 2$  can the numbers  $1$  to  $16$  be written each in one square of a squared  $4\times 4$  paper such that the  $8$  sums of the numbers in rows and columns are all different and divisible by  $n$ ?

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