
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
Let $\overrightarrow{e_{1}}$ and $\overrightarrow{e_{2}}$ be two non-collinear, non-zero vectors. If $\overrightarrow{AB} = 3\overrightarrow{e_{1}} + k\overrightarrow{e_{2}}$, $\overrightarrow{BC} = 4\overrightarrow{e_{1}} + \overrightarrow{e_{2}}$, $\overrightarrow{CD} = 8\overrightarrow{e_{1}} - 9\overrightarrow{e_{2}}$, and points A, B, D are collinear, find the value of the real number $k$.

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