
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 $\mathbf{Q},$ $\mathbf{P} \mathbf{Q}$ results in swapping the second row and third row of $\mathbf{Q},$ and tripling the first row of $\mathbf{Q}.$ In other words,
\[\mathbf{P} \begin{pmatrix} a & b & c \\ d & e & f \\ g & h & i \end{pmatrix} = \begin{pmatrix} 3a & 3b & 3c \\ g & h & i \\ d & e & f \end{pmatrix}.\]

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