
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
If \( \mathbf{B} = \begin{pmatrix} x & y & z \\ p & q & r \\ s & t & u \end{pmatrix} \), and \( \mathbf{B}^T = \mathbf{B}^{-1} \) such that \( x = \frac{1}{3} \), find \( x^2 + y^2 + z^2 + p^2 + q^2 + r^2 + s^2 + t^2 + u^2 \).

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