
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 and  $p$  a fixed prime. We have a deck of  $n$  cards, numbered  $1,\ 2,\ldots,\ n$  and  $p$  boxes for put the cards on them. Determine all posible integers  $n$  for which is possible to distribute the cards in the boxes in such a way the sum of the numbers of the cards in each box is the same.

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