
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
\[
\mathbf{N} \mathbf{a} = \begin{pmatrix} 4 \\ 5 \end{pmatrix} \quad \text{and} \quad \mathbf{N} \mathbf{b} = \begin{pmatrix} -3 \\ -7 \end{pmatrix}.
\]
Compute \(\mathbf{N} (2\mathbf{a} - 4\mathbf{b}).\)

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