
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
If $\overrightarrow{e_{1}}$ and $\overrightarrow{e_{2}}$ are two non-collinear vectors, given that $\overrightarrow{AB}=2 \overrightarrow{e_{1}}+k \overrightarrow{e_{2}}$, $\overrightarrow{CB}= \overrightarrow{e_{1}}+3 \overrightarrow{e_{2}}$, $\overrightarrow{CD}=2 \overrightarrow{e_{1}}- \overrightarrow{e_{2}}$, and points $A$, $B$, $D$ are collinear, then $k=$ \_\_\_\_\_\_.

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