
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 matrix \(\mathbf{N}\) that triples every element of a 2x2 matrix. In other words,
\[
\mathbf{N} \begin{pmatrix} a & b \\ c & d \end{pmatrix} = \begin{pmatrix} 3a & 3b \\ 3c & 3d \end{pmatrix}.
\]
If no such matrix \(\mathbf{N}\) exists, then enter the zero matrix.

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