
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 an increasing function defined on the interval $(-1, +\infty)$, and let $f(xy) = f(x) + f(y)$. If $f(3)=1$ and $f(a) > f(a-1) + 2$,  
find:  
(1) the value of $f(9)$,  
(2) the range of values for $a$.

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