
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  $m$  and  $n$  two given integers. Ana thinks of a pair of real numbers  $x$ ,  $y$  and then she tells Beto the values of  $x^m+y^m$  and  $x^n+y^n$ , in this order. Beto's goal is to determine the value of  $xy$  using that information. Find all values of  $m$  and  $n$  for which it is possible for Beto to fulfill his wish, whatever numbers that Ana had chosen. 

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