
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 that the function $y=f(x)$ is an increasing function defined on the interval $(0, +\infty)$, and for any $x > 0$, $y > 0$, it satisfies $f(xy) = f(x) + f(y)$, and it is known that $f(2) = 1$.  
(1) Find the values of $f(4)$ and $f\left(\frac{1}{2}\right)$.  
(2) Find the range of values for $x$ that satisfies $f(2x) - f(x-3) > 2$.

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