
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 any positive integer \( n \), let \( f(n) \) be the number of subsets of \(\{1, 2, \ldots, n\}\) whose sum is equal to \( n \). Does there exist infinitely many positive integers \( m \) such that \( f(m) = f(m+1) \)? (Note that each element in a subset must be distinct.)

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