
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 two vectors $a=(\lambda+2, \lambda^{2}-\cos ^{2}\alpha)$ and $b=(m, \frac{m}{2}+\sin \alpha)$, where $\lambda$, $m$, and $\alpha$ are real numbers. If $a=2b$, find the range of values for $\frac{\lambda}{m}$.

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