
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
Given a matrix $\mathbf{M}$ such that $\mathbf{M} \mathbf{i} = \begin{pmatrix} -1 \\ 4 \\ 9 \end{pmatrix},$ $\mathbf{M} \mathbf{j} = \begin{pmatrix} 6 \\ 2 \\ -3 \end{pmatrix},$ and $\mathbf{M} \mathbf{k} = \begin{pmatrix} 0 \\ -7 \\ 5 \end{pmatrix},$ find $\mathbf{M}$. Additionally, determine the vector that results when $\mathbf{M}$ is applied to $\mathbf{u} = \mathbf{i} + 2\mathbf{j} - \mathbf{k}$.

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