
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 $g(x) = \frac{3x-2}{x+3}$. Find an expression for $g^{-1}(x)$ in the form $g^{-1}(x) = \frac{ax+b}{cx+d}$ and determine the ratio $\frac{a}{c}$.

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