
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 $\mathbf{B}^{-1} = \begin{pmatrix} 3 & 7 \\ -2 & -4 \end{pmatrix},$ find the inverse of $(\mathbf{B}\mathbf{P})^2$ where $\mathbf{P} = \begin{pmatrix} 1 & 0 \\ 0 & 2 \end{pmatrix}$.

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