
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
In the set $\{1, 2, \cdots, n\}$, among the subsets with $m$ elements, a subset is called an even-set if the sum of its elements is even, and an odd-set if the sum of its elements is odd. Find the difference in the number of even-sets and odd-sets, denoted by $f(n, m)$.

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