
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. Calculate the definite integrals of the following functions: (1) $∫_0^2 (3x^2+4x^3) \, dx$; (2) $∫_0^1 (e^x+2x) \, dx$
2. Find the derivatives of the following functions: (1) $y = \frac{x^2+\sin(2x)}{e^x}$; (2) $y = \ln\left(\frac{2x+1}{2x-1}\right)$ for $x > \frac{1}{2}$

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