
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 the matrix:
\[\mathbf{N} = \begin{pmatrix} x & 2y & 0 \\ -x & y & z \\ x & -y & z \end{pmatrix}\]
It is known that \(\mathbf{N}^T \mathbf{N} = \mathbf{I}\). Find \(x^2 + y^2 + z^2\).

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