
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
Determine the value of $k$ such that the lines defined by the equations
\[\begin{pmatrix} 1 \\ 3 \end{pmatrix} + t \begin{pmatrix} 2 \\ -5 \end{pmatrix}\]
and
\[\begin{pmatrix} -1 \\ 4 \end{pmatrix} + s \begin{pmatrix} 3 \\ k \end{pmatrix}\]
do not intersect for any real numbers $t$ and $s$.

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