
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
\[\mathbf{M} \mathbf{u} = \begin{pmatrix} 2 \\ -2 \end{pmatrix}, \quad \mathbf{M} \mathbf{v} = \begin{pmatrix} 3 \\ 1 \end{pmatrix}, \quad \text{and} \quad \mathbf{M} \mathbf{w} = \begin{pmatrix} -1 \\ 4 \end{pmatrix}.\]
Compute \(\mathbf{M} (3\mathbf{u} - \mathbf{v} + 2\mathbf{w}).\)

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