
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) $\int x \cos x \, dx$
2) $\int \frac{\ln x}{x^{3}} \, dx$
3) $\int x \operatorname{arctg} x \, dx$
4) $\int \arcsin x \, dx$
5) $\int x^{2} e^{3 x} \, dx$
6) $\int e^{-x} \cos \frac{x}{2} \, dx$

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