
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 vectors $\overrightarrow{a}=(λ+2,λ^{2}- \sqrt {3}\cos 2α)$ and $\overrightarrow{b}=(m, \frac {m}{2}+\sin α\cos α)$, 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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