
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 function values for $f(x)$;
(2) Let $g(x) = \frac{ax^2 - 3x + 3}{x}$, where $a > 0$. If for all $s \in (0, +\infty)$ and $t \in \mathbb{R}$, the inequality $g(s) \geq f(t)$ holds true, find the range of values for the real number $a$.

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