
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 $\mathbf{M}$ that satisfies $\mathbf{M}(2\mathbf{i}) = \begin{pmatrix} 4 \\ 6 \\ -16 \end{pmatrix}$, $\mathbf{M}\mathbf{j} = \begin{pmatrix} 5 \\ 0 \\ -5 \end{pmatrix}$, and $\mathbf{M}(3\mathbf{k}) = \begin{pmatrix} 30 \\ -6 \\ 12 \end{pmatrix}$, find the matrix $\mathbf{M}$.

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