
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 vector $\overrightarrow{e_{1}} \neq \overrightarrow{0}, \lambda \in R$, $\overrightarrow{a} = \overrightarrow{e_{1}} + \lambda \overrightarrow{e_{2}}$, $\overrightarrow{b} = 2 \overrightarrow{e_{1}}$, if $\overrightarrow{a}$ and $\overrightarrow{b}$ are collinear, determine the condition on the vectors $\overrightarrow{e_1}$ and $\overrightarrow{e_2}$.

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