
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 $\mathbf{N}$ be a matrix and let $\mathbf{a}$ and $\mathbf{b}$ be vectors such that
\[
\mathbf{N} \mathbf{a} = \begin{pmatrix} 3 \\ 2 \end{pmatrix} \quad \text{and} \quad \mathbf{N} \mathbf{b} = \begin{pmatrix} 4 \\ 1 \end{pmatrix}.
\]
Compute $\mathbf{N} (2\mathbf{a} - 4 \mathbf{b}).$

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