
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 of the following functions:

1. \( z = x^3 + x^2 y + y^3 \)

2. \( f(x, y) = \sqrt{x^2 - y^2} \) at the point \((5, -3)\)

3. \( \varphi(x, y) = 2xy \) at the point \((0, 3)\)

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