
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 partial derivatives: 

1) $\frac{\partial z}{\partial u}$ and $\frac{\partial z}{\partial v}$, given \( z = \operatorname{arctg}\left(x^{2} y^{2}\right) \), \( x = v \sin u \), \( y = u \cos v \).

2) $\frac{\partial z}{\partial x}$ and $\frac{\partial z}{\partial y}$, given \( z = f(x^{2} + y^{2}, x^{2} y^{2}) \).

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