
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 \(\mathbf{M}\) be a matrix, and let \(\mathbf{v}\) and \(\mathbf{w}\) be vectors such that:
\[
\mathbf{M} \mathbf{v} = \begin{pmatrix} 1 \\ 4 \\ 2 \end{pmatrix} \quad \text{and} \quad \mathbf{M} \mathbf{w} = \begin{pmatrix} 0 \\ -1 \\ 3 \end{pmatrix}.
\]
Compute \(\mathbf{M} (2\mathbf{v} - 4\mathbf{w})\).

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