
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 that the domains of $f(x)$ and $g(x)$ are both $\mathbf{R}$, $f(x)$ is an even function, $g(x)$ is an odd function, and $f(x) + g(x) = \frac{1}{x^{2}-x+1}$, determine the range of $\frac{f(x)}{g(x)}$.

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