
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 $f(x) = |x|$, determine which of the following functions is equal to the function $y = f(x)$;
$(1) g(x) = (\sqrt{x})^2$; $(2) h(x) = \sqrt{x^2}$; $(3) s(x) = x$; $(4) y = \begin{cases} x, & x \geq 0 \\ -x, & x < 0 \end{cases}$

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