
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
Let $\overline{ab}$ be a two-digit integer. A positive integer is a relative of $\overline{ab}$ if:

i) The unit digit of $n$ is also $b$.

ii) The other digits of $n$ are non-zero and their sum is $a$.

For example, the relatives of 31 are 31, 121, 211, and 1111. Find all two-digit numbers that divide all their relatives.

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