
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 real numbers \( x, y \) and \( z \) are a solution \( (x, y, z) \) of the equation \( \left(x^{2}-9\right)^{2}+\left(y^{2}-4\right)^{2}+\left(z^{2}-1\right)^{2}=0 \). How many different possible values are there for \( x+y+z \)?

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