
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
Let $\mathbf{v}_0$ be a vector. The vector $\mathbf{v}_0$ is initially projected onto $\begin{pmatrix} 4 \\ 2 \end{pmatrix},$ resulting in the vector $\mathbf{v}_1.$ Subsequently, $\mathbf{v}_1$ is then projected onto $\begin{pmatrix} -1 \\ 2 \end{pmatrix},$ resulting in the vector $\mathbf{v}_2.$ Find the matrix that converts $\mathbf{v}_0$ to $\mathbf{v}_2.$

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