
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 $\overrightarrow{OA}=(\lambda\cos \alpha,\lambda\sin \alpha)(\lambda\neq 0)$, $\overrightarrow{OB}=(-\sin \beta,\cos \beta)$, where $O$ is the coordinate origin.
(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 $\lambda$ that makes $| \overrightarrow{BA}|\geqslant 2| \overrightarrow{OB}|$ hold.

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