
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
Calculate the integrals:

1) \(\int_{2}^{3} 3 x^{2} \, dx\)

2) \(\int_{0}^{1}\left(1+e^{\frac{x}{4}}\right) \, dx\)

3) \(\int_{-1}^{7} \frac{1}{\sqrt{3 t+4}} \, dt\)

4) \(\int_{0}^{\frac{\pi}{2 a}} (x+3) \sin(a x) \, dx\)

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