
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) \(\int(x+2) \ln x \, dx\)
2) \(\int x^2 \arcsin x \, dx\)
3) \(\int \arccos x \, dx\)
4) \(\int e^x \sin x \, dx\)
5) \(\int \left(x^2 + 2x + 1\right) \sin 3x \, dx\)
6) \(\int x^2 e^{3x} \, dx\)

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