
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:
\[\begin{pmatrix} -2 + r \\ 5 - 3kr \\ 0 + kr \end{pmatrix}\] 
and
\[\begin{pmatrix} 2t \\ 2 + 2t \\ -2t \end{pmatrix}.\]
Determine the value of $k$ such that the lines are coplanar.

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