
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) $y=(x+1)^2(x-1)$;  
(2) $y=x^2\sin x$;  
(3) $y=\frac{e^x+1}{e^x-1}$;  
(4) $f(x)=\frac{e^x}{x-2}$.

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