
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 doubles the first row and quadruples the second row of a matrix. Specifically,
\[\mathbf{N} \begin{pmatrix} x & y \\ z & w \end{pmatrix} = \begin{pmatrix} 2x & 2y \\ 4z & 4w \end{pmatrix}.\]
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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