
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
Given that $\overrightarrow{e\_1}$ and $\overrightarrow{e\_2}$ are two non-collinear vectors, $\overrightarrow{AB} = 2\overrightarrow{e\_1} - 8\overrightarrow{e\_2}$, $\overrightarrow{CB} = \overrightarrow{e\_1} + 3\overrightarrow{e\_2}$, and $\overrightarrow{CD} = 2\overrightarrow{e\_1} - \overrightarrow{e\_2}$. If $\overrightarrow{BF} = 3\overrightarrow{e\_1} - k\overrightarrow{e\_2}$ and points $B$, $D$, and $F$ are collinear, find the value of $k$.

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