
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
Find the integrals:
1) \(\int \frac{d x}{\sqrt[3]{5 x}}\)
2) \(\int \frac{d t}{\sqrt{3-4 t^{2}}}\)
3) \(\int \cos 3 \varphi \, d \varphi\)
4) \(\int e^{-\frac{x}{2}} \, d x\)
5) \(\int \sin (a x+b) \, d x\)
6) \(\int \frac{1}{5 x+4} \, d x\)

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