
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
Calculate the values of the partial derivatives of the given functions at the specified argument values:
1) \( f(\alpha, \beta) = \cos(m \alpha - n \beta), \quad \alpha = \frac{\pi}{2m}, \beta = 0 \);
2) \( z = \ln(x^{2} - y^{2}), \quad x = 2, y = -1 \).

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