
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
The ellipse \( x^{2} + 2y^{2} = 3 \) is rotated one full revolution around the y-axis to form a surface of revolution \(\Sigma\). Let \( P(x, y, z) \) be a point on \(\Sigma\). Then \( x^{2} + 2y^{2} + z^{2} = \quad \).

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