
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 \(g(x)\) satisfies
\[ c^3 g(d) = d^3 g(c) \] for all real numbers \(c\) and \(d\). If \(g(3) \neq 0\), find
\[\frac{g(6) - g(2)}{g(3)}.\]

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