
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 \( g(x) = \frac{1}{cx+d} \) where \( c \) and \( d \) are nonzero constants. Find all solutions to \( g^{-1}(x) = -2 \). Express your answer in terms of \( c \) and/or \( d \).

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