
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
Two lines are parameterized by the vectors 
\[\begin{pmatrix} 2 + 3s \\ -1 - 2ks \\ 4 + ks \end{pmatrix}\]
and
\[\begin{pmatrix} -t \\ 2 + 3t \\ 5 - 2t \end{pmatrix}.\]
Determine the value of \( k \) for which these lines are coplanar.

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