
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
\( f \) is a function from the integers to \(\{1, 2, 3, \ldots , n\} \) such that \( f(A) \) and \( f(B) \) are unequal whenever \( A \) and \( B \) differ by 5, 7, or 12. What is the smallest possible \( n \)?

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