
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
The line \(y = \frac{4x - 7}{5}\) is parameterized in the form
\[
\begin{pmatrix} x \\ y \end{pmatrix} = \mathbf{v} + t \mathbf{d},
\]
so that for \(x \ge 4,\) the distance between \(\begin{pmatrix} x \\ y \end{pmatrix}\) and \(\begin{pmatrix} 4 \\ 2 \end{pmatrix}\) is \(t.\) Find \(\mathbf{d}.\)

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