
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 function defined on $(0,+\infty)$. For any $x, y$ in its domain, it satisfies $f(xy)=f(x)+f(y)$, and $f(x) > 0$ when $x > 1$.

1. Write a function that meets the requirements and conjecture the monotonicity of $f(x)$ on $(0,+\infty)$.
2. If $f(2)=1$, solve the inequality $f(x)+f(x-3)\leqslant 2$.

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