
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 $\mathbf{B} = \begin{pmatrix} p & q \\ r & s \end{pmatrix}$, then its transpose is given by
\[\mathbf{B}^T = \begin{pmatrix} p & r \\ q & s \end{pmatrix}.\]
Given that $\mathbf{B}^T = 2\mathbf{B}^{-1}$, find $p^2 + q^2 + r^2 + s^2.$

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