
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 series expansion of the function $\operatorname{arctg} x$, starting from its expression in the form of an integral: $\operatorname{arctg} x=\int_{0}^{x} \frac{d t}{1+t^{2}}$, by expanding the integrand in a Maclaurin series and integrating term-by-term.

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