
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
By expanding the integrand in a Maclaurin series and integrating term by term, find the series expansions of the following integrals:
1) $\int \sin x^{2} \, dx$;
2) $\int \sqrt{x} e^{x} \, dx$;
3) $\int \sqrt{1-x^{3}} \, dx$.

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