
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 $\overrightarrow{e\_1} = (1, 0)$, $\overrightarrow{e\_2} = (0, 1)$, $\overrightarrow{a} = \overrightarrow{e\_1} - 2\overrightarrow{e\_2}$, and $\overrightarrow{b} = k\overrightarrow{e\_1} + \overrightarrow{e\_2}$, find the value of $k$ that satisfies the condition $\overrightarrow{a} \parallel \overrightarrow{b}$.

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