
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 positive integers  $b$  with the following property: there exists positive integers  $a,k,l$  such that  $a^k + b^l$  and  $a^l + b^k$  are divisible by  $b^{k+l}$  where  $k \neq l$ .

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