
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 integral \(\iint_{D}(x + 2y) \, dx \, dy\), where the region \(D\) is bounded by the parabolas \(y = x - x^{2}\), \(y = 1 - x^{2}\), and the \(Oy\)-axis.

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