
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 $\mathbf{N}$, $\mathbf{M} \mathbf{N}$ results in the first row being tripled and swapped with the second row, which is scaled by a factor of 2, and the third row being tripled. In other words,
\[
\mathbf{M} \begin{pmatrix} a & b & c \\ d & e & f \\ g & h & i \end{pmatrix} = \begin{pmatrix} 2d & 2e & 2f \\ 3a & 3b & 3c \\ 3g & 3h & 3i \end{pmatrix}.
\]

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