
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 $y=f(x)$ has a domain of $(0, +\infty)$, $f(8)=3$, and for any positive numbers $x_1$, $x_2$, it always holds that $f(x_1x_2)=f(x_1)+f(x_2)$, write a function that satisfies these conditions.

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