
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
Write the domain of the following functions:
(1) \( y=\frac{2x^2-1}{x^2+3} \);
(2) \( y=\sqrt{-x^2+3x-2} \);
(3) \( y=\frac{\sqrt{x+3}}{x-1} \);
(4) \( y=\frac{2x}{\sqrt{2x-4}-\sqrt{5-x}} \).

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