
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 two non-collinear vectors, $\overrightarrow a=\overrightarrow{{e_1}}+2\overrightarrow{{e_2}}$, $\overrightarrow b=2\overrightarrow{{e_1}}-k\overrightarrow{{e_2}}$. If $\overrightarrow a$ and $\overrightarrow b$ are collinear vectors, the value of the real number $k$ is ______.

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