
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 derivatives of the composite functions:

1) \( y = u^{2} e^{v}, \, u = \sin x, \, v = \cos x \)
2) \( p = u^{v}, \, u = \ln (x - y), \, v = e^{\frac{x}{y}} \)
3) \( z = x \sin v \cos \omega, \, v = \ln (x^{2} + 1), \, \omega = -\sqrt{1 - x^{2}} \)

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