
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  $n> 2$  be an integer. A child has  $n^2$  candies, which are distributed in  $n$  boxes. An operation consists in choosing two boxes that together contain an even number of candies and redistribute the candy from those boxes so that both contain the same amount of candy. Determine all the values of  $n$  for which the child, after some operations, can get each box containing  $n$  candies, no matter which the initial distribution of candies is.

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