
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
Given a $3 \times 3$ matrix $\mathbf{B} = \begin{pmatrix} p & q & r \\ s & t & u \\ v & w & x \end{pmatrix}$, and its transpose is defined by $\mathbf{B}^T = \begin{pmatrix} p & s & v \\ q & t & w \\ r & u & x \end{pmatrix}$. Given that $\mathbf{B}^T = \mathbf{B}^{-1}$, find $p^2 + q^2 + r^2 + s^2 + t^2 + u^2 + v^2 + w^2 + x^2.$

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