
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
The function $g$ has the property that for each real number $x$ in its domain, $x^2$ is also in its domain and \[
g(x) + g(x^2) = x^2.
\]
What is the largest set of real numbers that can be in the domain of $g$?

(a) $\{x \mid x \neq 0\}$

(b) $\{x \mid x < 0\}$

(c) $\{x \mid x > 0\}$

(d) $\{x \mid x \neq -1 \text{ and } x \neq 0 \text{ and } x \neq 1\}$

(e) $\{1, -1\}$

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