
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  $\{1, 2, . . . , n\}$  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}
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