
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
Given the function $f(x) = 3^x$, its inverse function is denoted as $y = g(x)$.
(1) Calculate the value of $g(4) + g(8) - g\left(\frac{32}{9}\right)$;
(2) Solve the inequality $g\left(\frac{x}{1-x}\right) < f(0)$.

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