
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
1) Compute the surface integral:
\[ I = \iint_{\sigma} \sqrt[4]{x^{2}+y^{2}} \, dx \, dy, \]
where \(\sigma\) is the lower side of the circle \(x^{2}+y^{2} \leqslant a^{2}\).

2) Compute the surface integral:
\[ J = \iint_{T} 2 \, dx \, dy + y \, dx \, dz - x^{2}z \, dy \, dz, \]
where \(T\) is the external part of the ellipsoid \(4x^{2} + y^{2} + 4z^{2} = 4\) located in the first octant.

3) Compute the surface integral:
\[ K = \oiint_{-W} y \, dx \, dz, \]
where \(W\) is the surface of the tetrahedron bounded by the plane \(x + y + z = 1\).

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