
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 $f(x)$ is $(0,+∞)$, and it satisfies $f(xy)=f(x)+f(y)$, $f( \frac {1}{2})=1$. If for $0 < x < y$, we always have $f(x) > f(y)$,
$(1)$ Find $f(1)$;
$(2)$ Solve the inequality $f(-x)+f(3-x)\geqslant -2$.

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