
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 over the regions bounded by the specified lines:

a) \(\iint x^{2} y \, dx \, dy\); \(y=0\); \(y=\sqrt{2ax - x^{2}}\);

b) \(\iint_{\Omega} \sin(x+y) \, dx \, dy\); \(y=0\); \(y=x\); \(x+y=\frac{\pi}{2}\);

c) \(\iint_{\Omega} x^{2}(y-x) \, dx \, dy\); \(x=y^{2}\); \(y=x^{2}\).

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