
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
(1) Find the domain of the function $f(x)= \sqrt {x^{2}+x-1}+ \frac {1}{x^{2}-2x+1}$;
(2) Find the domain of the function $f(x)= \frac { \sqrt {|x-2|-1}}{(x-3)(x-1)}$;
(3) Given that the domain of the function $y=f(x^{2}-1)$ is $[-1,3]$, find the domain of $y=f(2x+1)$.

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