
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. \( z = 4 - x - 2y \)
2. \( p = \frac{3}{x^2 + y^2} \)
3. \( z = \sqrt{1 - x^2 - y^2} \)
4. \( q = \frac{1}{\sqrt{xy}} \)
5. \( u = \frac{x^2 y}{2x + 1 - y} \)
6. \( v = \arcsin(x + y) \)

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