
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  $(a,b)$  such that there exists a finite set  $S$  satisfying that any positive integer can be written in the form   $$ n = x^a + y^b + s $$  where  $x,y$  are nonnegative integers and  $s \in S$ *CSJL*

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