
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
Consider two lines defined by the parametric equations \(\begin{pmatrix} 1 \\ 3 \end{pmatrix} + t \begin{pmatrix} 5 \\ -8 \end{pmatrix}\) and \(\begin{pmatrix} -1 \\ 4 \end{pmatrix} + s \begin{pmatrix} 2 \\ k \end{pmatrix}\). Find the value of \( k \) such that these lines do not intersect.

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