
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

Using series, compute the approximate values of the following integrals with an accuracy up to 0.0001:

$$
I_{1}=\int_{0}^{\frac{1}{3}} \frac{d t}{\sqrt{1+t^{2}}} ; \quad I_{2}=\int_{0}^{1} \cos \pi x \, d x ; \quad I_{3}=\int_{1}^{1.5} \frac{1}{v} \operatorname{arctg} \frac{v}{4} \, d v
$$

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