
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 $\mathbf{N} \mathbf{i} = \begin{pmatrix} 1 \\ 4 \\ -3 \end{pmatrix}$, $\mathbf{N} \mathbf{j} = \begin{pmatrix} -2 \\ 6 \\ 5 \end{pmatrix}$, and $\mathbf{N} \mathbf{k} = \begin{pmatrix} 0 \\ 1 \\ 2 \end{pmatrix}$, given that the determinant of $\mathbf{N}$ is non-zero.

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