
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 $\vec{e_1}$ and $\vec{e_2}$ are non-collinear vectors, $\vec{AB} =2 \vec{e_1} + \vec{e_2}$, $\vec{BC} =- \vec{e_1} +3 \vec{e_2}$, $\vec{CD} =\lambda \vec{e_1} - \vec{e_2}$, and points $A$, $B$, $D$ are collinear, determine the value of $\lambda$.

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