
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) \(z = x + y - 1\)
2) \(f(x, y) = \frac{x + 1}{x^{2} + y^{2}}\)
3) \(z = \sqrt{4 - x^{2} - y^{2}}\)
4) \(u = \frac{1}{\sqrt{9 - x^{2} - y^{2}}}\)
5) \(\varphi(x, y) = x - \arcsin y\)
6) \(z = \frac{1}{\sqrt{x y}}\)

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