
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
Suppose that $f(x) = ax+b$ and $g(x) = -4x+6$. If $h(x) = f(g(x))$ and $h^{-1}(x) = x + 9$, find the value of $2a - 3b$.

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