
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
Find all  $n \in N$  for which the value of the expression  $x^n+y^n+z^n$  is constant for all  $x,y,z \in R$  such that  $x+y+z=0$  and  $xyz=1$ .

D. Bazylev

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