
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 domain of the function $y=f(x)$ is $(0,+\infty)$, when $x > 1$, $f(x) < 0$, and for any $x$, $y\in R$, it always holds that $f(xy)=f(x)+f(y)$. Determine the solution set for the inequality $f(x)+f(x-2)\geqslant f(8)$.

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