
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
A line is parameterized by a parameter $t,$ so that the vector on the line at $t = 0$ is $\begin{pmatrix} 2 \\ -1 \\ 3 \end{pmatrix},$ and the vector on the line at $t = 4$ is $\begin{pmatrix} 6 \\ 7 \\ -1 \end{pmatrix}.$ Find the vector on the line at $t = 6.$

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