
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 $\mathbf{u}$, $\mathbf{v}$, and $\mathbf{w}$ be vectors such that:
\[
\mathbf{M} \mathbf{u} = \begin{pmatrix} -3 \\ 4 \end{pmatrix}, \quad \mathbf{M} \mathbf{v} = \begin{pmatrix} 2 \\ -7 \end{pmatrix}, \quad \text{and} \quad \mathbf{M} \mathbf{w} = \begin{pmatrix} 9 \\ 0 \end{pmatrix}.
\]
Compute $\mathbf{M} (3\mathbf{u} - 4\mathbf{v} + 2\mathbf{w})$.

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