
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
In 3D space, a line is parameterized by $t$ such that at $t = 1$, the vector position is $\begin{pmatrix} 2 \\ 0 \\ -3 \end{pmatrix}$, at $t = 2$ it is $\begin{pmatrix} 7 \\ -2 \\ 1 \end{pmatrix}$, and at $t = 4$ it is $\begin{pmatrix} 17 \\ -6 \\ 9 \end{pmatrix}$. Find the vector position at $t = -2$.

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