
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
Since vectors $\vec{e_1}$ and $\vec{e_2}$ are non-collinear vectors in a plane, and given that $\vec{AB} = \vec{e_1} - k\vec{e_2}$, $\vec{CB} = 2\vec{e_1} + \vec{e_2}$, and $\vec{CD} = 3\vec{e_1} - \vec{e_2}$, find the value of $k$.

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