
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 $xoy$, a line $l$ passes through the point $P(-3,0)$, and its inclination angle is $\alpha$. Taking the origin $O$ as the pole and the positive half-axis of $x$ as the polar axis, a polar coordinate system is established with the same unit of length as the Cartesian coordinate system $xoy$. The polar equation of curve $C$ is given by $\rho^{2}-2\rho \cos \theta -3=0$.

(Ⅰ) If line $l$ has a common point with curve $C$, find the range of values for the inclination angle $\alpha$;

(Ⅱ) Let $M(x,y)$ be any point on curve $C$, find the range of values for $x+y$.

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