
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 following functions:
1) \( y = x^x \);
2) \( r = (\cos \alpha)^{\sin 2 \alpha} \);
3) \( s = \frac{2t}{\sqrt{1 - t^2}} \);
4) \( R = (x - 1) \sqrt[3]{(x + 1)^2 (x - 2)} \).

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