
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 $g(x) = \displaystyle \frac{1}{2ax + b}$, where $a$ and $b$ are non-zero constants and $a \neq b$. Find all solutions to $g^{-1}(x) = 0$. Express your answer in terms of $a$ and/or $b$.

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