
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
In the Cartesian coordinate system xOy, the line l passes through point A (-1, 0) with an inclination angle of α. Taking the origin O as the pole and the non-negative half of the x-axis as the polar axis, a polar coordinate system is established with the same unit of length as in the Cartesian coordinate system xOy. The polar equation of curve C is $\rho^2=6\rho\cos\theta-5$.
(Ⅰ) If the line l and the curve C have a common point, find the range of the inclination angle α.
(Ⅱ) Let B(x, y) be any point on curve C, find the range of $\sqrt{3}x+y$.

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