
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 in 3D space given by:
\[
\begin{pmatrix} 3 \\ 2 \\ 6 \end{pmatrix} + t \begin{pmatrix} 2 \\ -m \\ 1 \end{pmatrix}
\]
and
\[
\begin{pmatrix} 4 \\ 5 \\ 8 \end{pmatrix} + u \begin{pmatrix} m \\ 3 \\ 2 \end{pmatrix}
\]
Determine all possible values of $m$ such that the lines are coplanar.

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