
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
The function $f\left(x\right)$ is an increasing function defined on $\left(0,+\infty \right)$. If for any positive real numbers $x$ and $y$, it always holds that $f\left(xy\right)=f\left(x\right)+f\left(y\right)$, and $f\left(3\right)=1$, then the solution set of the inequality $f\left(x\right)+f\left(x-8\right) \lt 2$ is ______.

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