
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 circle $C$: $\begin{cases} x=1+\cos \theta \\ y=\sin \theta \end{cases}(\theta$ is a parameter $)$ and line $l$: $\begin{cases} x=2+t\cos \alpha \\ y=\sqrt {3}+t\sin \alpha \end{cases}(\text{where } t \text{ is a parameter, } \alpha \text{ is the angle of inclination of line } l )$
(1) When $\alpha= \dfrac {2π}{3}$, find the minimum distance from a point on the circle to line $l$;
(2) When line $l$ intersects with circle $C$, find the range of values for $\alpha$.

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