
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 $f(x)$ be a monotonically increasing function defined on $(0, +\infty)$ with the property $f(xy) = f(x) + f(y)$, and given that $f(3) = 1$.
(1) Find $f(9)$;
(2) Solve the inequality $f(2x) > 2 + f(x - 2)$.

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