
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
$\overrightarrow{AB}=\overrightarrow{{e}_{1}}-\overrightarrow{{e}_{2}}$,$\overrightarrow{BC}=3\overrightarrow{{e}_{1}}+2\overrightarrow{{e}_{2}}$,$\overrightarrow{CD}=k\overrightarrow{{e}_{1}}+2\overrightarrow{{e}_{2}}$, and points $A$, $C$, $D$ are collinear. Find the value of k.

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