
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 $f(x) = |x|$, identify which of the following functions are identical to $f(x)$:

1. $y = \sqrt{x^2}$
2. $y = (\sqrt{x})^2$
3. $y = \frac{x^2}{x}$
4. $y = \begin{cases} x & \text{for } x>0 \\ -x & \text{for } x<0 \end{cases}$

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