
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
Define \( g \) by \( g(x)=3x-2 \). If \( g(x)=f^{-1}(x)-2 \) and \( f^{-1}(x) \) is the inverse of the function \( f(x)=ax+b \), find \( 3a+4b \).

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