
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
1) \( y = -\frac{\cos x}{\sin^2 x} + \ln \tan \frac{x}{2}; \; y' \) ?

2) \( y = \arcsin (\cos x); \; y' \) ?

3) \( r = \varphi^2 \arccos \frac{2}{\varphi} - 2 \sqrt{\varphi^2 - 4}; \) compute \( r'(2) \) and \( r'(-2) \).

4) \( y = \left| 1 - x^2 \right|; \) find \( y'\left( \frac{1}{2} \right), y'(-2) \) and the points where the function is not differentiable.

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