
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
For vectors \(\mathbf{v} = \begin{pmatrix} x \\ 4 \end{pmatrix}\) and \(\mathbf{w} = \begin{pmatrix} 8 \\ -2 \end{pmatrix}\),
\[\text{proj}_{\mathbf{w}} \mathbf{v} = \begin{pmatrix} 4 \\ -1 \end{pmatrix}.\]
Find \(x\).

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