
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 $(0,+\infty)$, with $f(2)=1$ and $f(xy)=f(x)+f(y)$.

(1) Find the value of $f(4)$.
(2) Find the range of $x$ that satisfies the inequality $f(x)+f(x-3) \leqslant 2$.

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