
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
Find the flux of the vector field \(\bar{p}=x \bar{i}-y^{2} \bar{j}+\left(x^{2}+z^{2}-1\right) \bar{k}\) through the surface \(\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}+\frac{z^{3}}{c^{2}}=1\) (ellipsoid) from inside this surface.

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