
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 \( y = \frac{2x - 4}{3} \) is parameterized in the form
\[
\begin{pmatrix} x \\ y \end{pmatrix} = \mathbf{v} + t \mathbf{d},
\]
so that for \( x \ge 2 \), the distance between \( \begin{pmatrix} x \\ y \end{pmatrix} \) and \( \begin{pmatrix} 2 \\ 0 \end{pmatrix} \) is \( t \). Find \( \mathbf{d} \).

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