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

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