
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 vectors $\overrightarrow {OA} = (\lambda \cos \alpha, \lambda \sin \alpha)$ (where $\lambda \neq 0$), and $\overrightarrow {OB} = (-\sin \beta, \cos \beta)$ with $O$ being the origin of the coordinates.
1. If $\lambda = 1$ and $\alpha = \frac{\pi}{2}$, $\beta = \frac{\pi}{3}$, find the angle between vectors $\overrightarrow {OA}$ and $\overrightarrow {OB}$.
2. If $\alpha - \beta = \frac{\pi}{2}$, find the range of values for $\lambda$ that satisfies $|\overrightarrow {BA}| \geq 2|\overrightarrow {OB}|$.

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