
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 derivative of the following functions.

$(1) y = \frac{1}{1-\sqrt{x}} + \frac{1}{1+\sqrt{x}}$; $(2) y = \frac{4-\sin x}{\cos x}$;
$(3) y = \ln \frac{x+3}{x+1}, (x > -1)$; $(4) y = e^{x-\cos x} + \frac{2}{x} - x^{3}$

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