
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 $\mathbf{P}$ such that for a $3 \times 3$ matrix $\mathbf{Q},$ $\mathbf{P} \mathbf{Q}$ is the result of rotating each row one position upwards (the first row moves to the place of the second row, the second row to the third, and the third row to the first) and tripling the original first row of $\mathbf{Q}$. In other words,
\[
\mathbf{P} \begin{pmatrix} a & b & c \\ d & e & f \\ g & h & i \end{pmatrix} = \begin{pmatrix} d & e & f \\ g & h & i \\ 3a & 3b & 3c \end{pmatrix}.
\]

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