
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 vector $\mathbf{u}$ such that:
\[\operatorname{proj}_{\begin{pmatrix} 3 \\ 2 \end{pmatrix}} \mathbf{u} = \begin{pmatrix} 6 \\ 4 \end{pmatrix}\]
and
\[\operatorname{proj}_{\begin{pmatrix} 1 \\ 4 \end{pmatrix}} \mathbf{u} = \begin{pmatrix} 2 \\ 8 \end{pmatrix}.\]

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