
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
Find the domains of the following functions:
1) \( y=\sqrt{3+2x} \)
2) \( f(x)=1+\sqrt{9-x^2} \)
3) \( \varphi(x)=\sqrt{\lg \frac{5x-x^2}{4}} \)
4) \( y=\sqrt{3-x}+\arccos \frac{x-2}{3} \)

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