
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
Consider the function \( f(x) = \frac{3x-2}{2x+4} \). The inverse of this function, \( f^{-1}(x) \), can also be written in the form \( f^{-1}(x) = \frac{ax + b}{cx + d} \) where \( a \), \( b \), \( c \), and \( d \) are real numbers. Determine the value of \( \frac{a}{c} \).

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