
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
Change the order of integration:

$$
I = \int_{0}^{1} dx \int_{0}^{x^{2}} f(x, y) \, dy + \int_{1}^{\sqrt{2}} dx \int_{0}^{\sqrt{2 - x^{2}}} f(x, y) \, dy
$$

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