
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 $3 \times 3$ matrix $\mathbf{M}$ such that for any $3 \times 3$ matrix $\mathbf{N},$ the matrix multiplication $\mathbf{M} \mathbf{N}$ results in a matrix where the first row of $\mathbf{N}$ is swapped with the third row and the second row of $\mathbf{N}$ is tripled. In other words, 
\[ \mathbf{M} \begin{pmatrix} a & b & c \\ d & e & f \\ g & h & i \end{pmatrix} = \begin{pmatrix} g & h & i \\ 3d & 3e & 3f \\ a & b & c \end{pmatrix}. \]

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