
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 $y = f(x)$ be a decreasing function defined on $(0, +\infty)$, satisfying $f(xy) = f(x) + f(y)$, and $f\left(\frac{1}{3}\right) = 1$.
(1) Find the values of $f(1)$, $f\left(\frac{1}{9}\right)$, and $f(9)$;
(2) If $f(x) - f(2-x) < 2$, determine the range of values for $x$.

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