
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 the function $g$ be defined for all non-zero real numbers $x$ such that
\[ g(x) + 3g\left(\frac{1}{x}\right) = 4x^2. \]
Find the real solutions to $g(x) = g(-x)$.

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