
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) $\int \frac{2 x \, dx}{x^{4}+3}$
2) $\int \frac{\sin x \, dx}{\sqrt{1+2 \cos x}}$
3) $\int \frac{x \, dx}{\sqrt[3]{x^{2}+a}}$
4) $\int \frac{\sqrt{1+\ln x}}{x} \, dx$
5) $\int \frac{d y}{\sqrt{e^{y}+1}}$
6) $\int \frac{d t}{\sqrt{\left(1-t^{2}\right)^{3}}}$


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