
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 vectors. Given $\overrightarrow{AB}=2\overrightarrow{e_1}+k\overrightarrow{e_2}$, $\overrightarrow{CD}=2\overrightarrow{e_1}-\overrightarrow{e_2}$, and $\overrightarrow{CB}=\overrightarrow{e_1}+3\overrightarrow{e_2}$. If 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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