
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
Let $\mathbf{B} = \begin{pmatrix} x & y \\ z & w \end{pmatrix}$ be an orthogonal matrix such that $\mathbf{B}^T = \mathbf{B}^{-1}$ and $\mathbf{B} \mathbf{B}^T = \mathbf{I}$. Additionally, assume that $x + y + z + w = 0$. Find the value of $x^2 + y^2 + z^2 + w^2$.

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