
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 $g$ be a function defined for all non-zero real numbers $x$, such that:
\[g(x) + 3g \left( \frac{1}{x} \right) = 6x^2.\]
Find all real solutions to $g(x) = g(-x)$.

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