
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
Consider the following four pairs of functions:
1. $f(x) = \sqrt{(x - 1)^2}, \quad g(x) = x - 1$,
2. $f(x) = \sqrt{x^2 - 1}, \quad g(x) = \sqrt{x + 1} \cdot \sqrt{x - 1}$,
3. $f(x) = (\sqrt{x - 1})^2, \quad g(x) = \sqrt{(x - 1)^2}$,
4. $f(x) = \sqrt{\frac{x^2 - 1}{x + 2}}, \quad g(x) = \frac{\sqrt{x^2 - 1}}{\sqrt{x + 2}}$,
Which pair(s) of functions are identical?

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