
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 $\overrightarrow{a}= \overrightarrow{e_{1}}-4 \overrightarrow{e_{2}}$ and $\overrightarrow{b}=2 \overrightarrow{e_{1}}+k \overrightarrow{e_{2}}$, where vectors $\overrightarrow{e_{1}}$ and $\overrightarrow{e_{2}}$ are not collinear, find the value of $k$ such that $\overrightarrow{a} \parallel \overrightarrow{b}$.

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