
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 $\overrightarrow{e_{2}}$ be two non-collinear vectors, $\overrightarrow{AB}=2\overrightarrow{e_{1}}+k\overrightarrow{e_{2}}$, $\overrightarrow{CB}=\overrightarrow{e_{1}}+3\overrightarrow{e_{2}}$, and $\overrightarrow{CD}=2\overrightarrow{e_{1}}-\overrightarrow{e_{2}}$, and points A, B, and D are collinear, find the value of k.

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