
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 $\overrightarrow{e_{1}}$ and $\overrightarrow{e_{2}}$ are non-collinear vectors, $\overrightarrow{AB}=2\overrightarrow{e_{1}}+\overrightarrow{e_{2}}$, $\overrightarrow{BC}=-\overrightarrow{e_{1}}+3\overrightarrow{e_{2}}$, $\overrightarrow{CD}=\lambda\overrightarrow{e_{1}}-\overrightarrow{e_{2}}$, and points $A$, $B$, and $D$ are collinear, determine the value of the real number $\lambda$.

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