
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
A pair of positive integers is called "compatible" if and only if one of the numbers is equal to the sum of the digits of the pair, and the other number is equal to the product of the digits of the pair. Try to find:
(1) All compatible pairs of positive integers within 100;
(2) All compatible pairs of positive integers within 1000, where one of the numbers is greater than 99.

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