
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 inverse of $f(x) = \frac{3x + 2}{x - 4}$ may be written in the form $f^{-1}(x)=\frac{ax + b}{cx + d}$, where $a$, $b$, $c$, and $d$ are real numbers. Find the value of $\frac{a}{c}$.

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