
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
For each positive integer  $n$  let  $s(n)$  denote the sum of the decimal digits of  $n$ . Find all pairs of positive integers  $(a, b)$  with  $a > b$  which simultaneously satisfy the following two conditions  $$ a \mid b + s(a) $$    $$ b \mid a + s(b) $$  *Proposed by Victor Domínguez*

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