
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 circle $C:\begin{cases} & x=1+\cos \theta \\\\ & y=\sin \theta \end{cases}$ (where $\theta$ is a parameter) and the line $l:\begin{cases} & x=2+t\cos \alpha \\\\ & y=\sqrt{3}+t\sin \alpha \end{cases}$ (where $t$ is a parameter and $\alpha$ is the slope angle of line $l$), find the range of values for $\alpha$ if line $l$ intersects with circle $C$.

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