
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 $\mathbf{u}_0$ be a vector. The vector $\mathbf{u}_0$ is projected onto $\begin{pmatrix} 4 \\ 2 \end{pmatrix}$, resulting in the vector $\mathbf{u}_1$. The vector $\mathbf{u}_1$ is then projected onto $\begin{pmatrix} 2 \\ 3 \end{pmatrix}$, resulting in the vector $\mathbf{u}_2$. Find the matrix that takes $\mathbf{u}_0$ to $\mathbf{u}_2$.

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