
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 $(0, +\infty)$ that satisfies $f(xy) = f(x) + f(y)$ and $f(3) = 1$. Find:  
(1) $f(1)$;  
(2) If $f(x) + f(x-8) \leq 2$, determine the range of values for $x$.

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