
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
Find the matrix $\mathbf{N}$ if it satisfies $\mathbf{N} \mathbf{i} = \begin{pmatrix} 4 \\ 6 \\ -16 \end{pmatrix},$ $\mathbf{N} \mathbf{j} = \begin{pmatrix} 0 \\ 10 \\ -4 \end{pmatrix},$ and $\mathbf{N} \mathbf{k} = \begin{pmatrix} 14 \\ -2 \\ 8 \end{pmatrix}.$

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