
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
Which two functions from the following four groups are the same?
(1) \( f(x) = |x| \), \( g(t) = \sqrt{t^2} \);
(2) \( f(x) = \sqrt{x^2} \), \( g(x) = (\sqrt[3]{x})^3 \);
(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}
user