
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
Calculate the double integrals and change the order of integration.

$$
\text{a) } \int_{0}^{2} dx \int_{0}^{3}\left(x^{2} + 2xy\right) dy
$$

b) $\int_{-2}^{0} dy \int_{0}^{y^{2}}(x+2y) dx$

c) $\int_{0}^{5} dx \int_{0}^{5-x} \sqrt{4 + x + y} dy$

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