
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 a positive integer $n$, let $f(n)$ denote the number obtained by reversing the digits of $n$ in decimal notation. (For example, $f(2500) = 52$ and $f(1456) = 6541$.) Find all positive integers $k$ such that, for any multiple $n$ of $k$, $k$ also divides $f(n)$.

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