
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 \( m \) and \( n \) be integers such that \( n > m \geq 2 \). Consider the set \( \{m, m+1, \cdots, n\} \) which is arbitrarily divided into two subsets. In at least one of the subsets, there must exist \( a, b, c \) (not necessarily different) such that \( a^b = c \). Find the smallest value of \( n \), denoted as \( f(m) \).

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