
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 pairs of positive integers  $(x,y)$  with the following property:
If  $a,b$  are relative prime and positive divisors of    $ x^3 + y^3$ , then   $a+b - 1$  is divisor of  $x^3+y^3$ .

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