
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
Given $f(n)=\frac{x_1+x_2+\cdots +x_n}{n}$, where $n$ is a positive integer, and $x_k=(-1)^{k+1}$, $k=1,2,\cdots,n$, calculate the set of possible values of $f(n)$.

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