
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 $f(x) = |x+1| - 2|x-1|$.

(1) Find the area of the triangle formed by the graph of $f(x)$ and the axis.

(2) Let $g(x) = \frac{x^2 - ax + 4}{x}$. If $g(s) \geq f(t)$ holds for all $s, t \in (0, +\infty)$, find the range of values for the real number $a$.

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