
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 a function $y=f(x)$ with domain $\mathbb{R}$ whose graph is symmetric about the point $(-1,0)$, let $y=g(x)$ be the inverse function of $y=f(x)$. If $x_1 + x_2 = 0$, then $g(x_1) + g(x_2) = \boxed{?}$.

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