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

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