
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 $P(-1,0)$, and its inclination angle is $\alpha$. In the polar coordinate system with the origin $O$ as the pole and the non-negative half-axis of $x$ as the polar axis (using the same unit of length), the polar equation of curve $C$ is $\rho^{2}-6\rho\cos \theta+1=0$.
- (I) If line $l$ has a common point with curve $C$, find the range of $\alpha$.
- (II) Let $M(x,y)$ be any point on curve $C$, find the range of $x+y$.

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