
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 $\mathbf{B}$ be a matrix such that
\[\mathbf{B} \begin{pmatrix} 10 \\ -4 \end{pmatrix} = \begin{pmatrix} 50 \\ -20 \end{pmatrix}.\] Find $\mathbf{B}^3 \begin{pmatrix} 10 \\ -4 \end{pmatrix}.$

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