
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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