
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 $g(n)=\frac{x_1+x_2+\cdots +x_n}{n}$, where $n$ is a positive integer and $x_k = 2(-1)^k$ for $k=1,2,\cdots,n$. Determine the set of possible values of $g(n)$.
A) $\{0\}$
B) $\{-\frac{2}{n}\}$
C) $\{0, -\frac{2}{n}\}$
D) $\{0, \frac{2}{n}\}$
E) $\{-2, 0\}$

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