
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 following integrals and verify the results by differentiation:
1) \(\int\left(x^{2}-2 \sin x+3 e^{x}\right) dx\),
2) \(\int\left(\sec^{2} x - 3 \cos x + 1\right) dx\),
3) \(\int\left(\csc^{2} x + 7 \sin x - 2\right) dx\).

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