
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 following line is parameterized so that its direction vector is of the form $\begin{pmatrix} a \\ 2 \end{pmatrix}$. Find $a$.

[asy]
unitsize(0.4 cm);

pair A, B, L, R;
int i, n;

for (i = -8; i <= 8; ++i) {
  draw((i,-8)--(i,8),gray(0.7));
  draw((-8,i)--(8,i),gray(0.7));
}

draw((-8,0)--(8,0),Arrows(6));
draw((0,-8)--(0,8),Arrows(6));

A = (3, -1);
B = (-1, 4);
L = extension(A, B, (0,8), (1,8));
R = extension(A, B, (0,-8), (1,-8));

draw(L--R, blue);

label("$x$", (8,0), E);
label("$y$", (0,8), N);
[/asy]

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