
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 such that
\[\mathbf{N} \mathbf{u} = \begin{pmatrix} 1 \\ 4 \end{pmatrix} \quad \text{and} \quad \mathbf{N} \mathbf{z} = \begin{pmatrix} 5 \\ -3 \end{pmatrix}.\]
Compute $\mathbf{N} (-2\mathbf{u} + 4 \mathbf{z}).$

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