
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
Among the following functions, identify which pairs represent the same function.

1. $f(x) = |x|, g(x) = \sqrt{x^2}$;
2. $f(x) = \sqrt{x^2}, g(x) = (\sqrt{x})^2$;
3. $f(x) = \frac{x^2 - 1}{x - 1}, g(x) = x + 1$;
4. $f(x) = \sqrt{x + 1} \cdot \sqrt{x - 1}, g(x) = \sqrt{x^2 - 1}$.

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