
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. Compute the definite integrals of the following functions:
   (1) $\int_{0}^{2}(3x^{2}+4x^{3})dx$;
   (2) $\int_{0}^{1}(e^{x}+2x)dx$

2. Compute the derivatives of the following functions:
   (1) $y=\frac{x^{2}+\sin 2x}{e^{x}}$
   (2) $y=\ln \frac{2x+1}{2x-1} (x > \frac{1}{2})$

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