
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 $\overrightarrow{OA}=(\lambda \cos \alpha, \lambda \sin \alpha)(\lambda \neq 0)$, $\overrightarrow{OB}=(-\sin \beta, \cos \beta)$, and $\overrightarrow{OC}=(1,0)$, where $O$ is the origin of the coordinate system.

(1) If $\lambda=2$, $\alpha = \frac{\pi}{3}$, $\beta \in (0,\pi)$, and $\overrightarrow{OA} \perp \overrightarrow{BC}$, find the value of $\beta$;

(2) If $|\overrightarrow{AB}|\geqslant 2|\overrightarrow{OB}|$ holds for any real numbers $\alpha$ and $\beta$, find the range of values for the real number $\lambda$.

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