
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 the following parameterizations of two lines:
\[\begin{pmatrix} 1 + 2s \\ 4 - 3ks \\ 5 + 2ks \end{pmatrix}\]
and 
\[\begin{pmatrix} -1 + 3t/2 \\ 3 + 2t \\ 8 - 3t \end{pmatrix}.\]
Determine the value of \( k \) if these lines are coplanar.

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