
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
Please use the rules of differentiation to find the derivatives of the following functions.  
(1) $y=e^{\sin x}$  
(2) $y= \frac{x+3}{x+2}$  
(3) $y=\ln(2x+3)$  
(4) $y=(x^2+2)(2x-1)$  
(5) $y=\cos\left(2x+ \frac{\pi}{3}\right)$．

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