
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 the function $f(x)=|x+2|-|x-1|$.
- $(1)$ Find the range of $f(x)$.
- $(2)$ Let $g(x)= \frac {ax^{2}-3x+3}{x}$ $(a > 0)$. If for any $s\in[1,+\infty)$ and $t\in[0,+\infty)$, $g(s)\geqslant f(t)$ always holds, find the range of the real number $a$.

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