
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
Consider a tilted three-dimensional ellipsoid whose major axis is aligned with a diagonal in the plane \(x-y\). The equation of the ellipsoid in its standard form is given by:
\[
\frac{(x - x_0)^2}{A^2} + \frac{(y - y_0)^2}{B^2} + \frac{(z - z_0)^2}{C^2} = 1.
\]
Find \(x_0 + y_0 + z_0 + A + B + C \) given the center of the ellipsoid is at \((-2, 3, 1)\), its semi-major axes are \(6, 4, 2\) along the \(x\), \(y\), and \(z\) directions, respectively.

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