
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 the vector $\overrightarrow{a} = (λ + 2, λ^2 - \sqrt{3} \cos{2α})$ and vector $\overrightarrow{b} = (m, \frac{m}{2} + \sin{α} \cos{α})$, where $λ$, $m$, and $α$ are real numbers. If $\overrightarrow{a} = 2\overrightarrow{b}$, determine the range of values for $\frac{λ}{m}$.

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