
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  $(a,b)$  of positive integers, such that for **every**  $n$  positive integer, the equality  $a^n+b^n=c_n^{n+1}$  is true, for some  $c_n$  positive integer. 

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