
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 $xoy$, line $l$ passes through point $P(-3, 0)$, and its inclination angle is $\alpha$. Taking the origin $O$ as the pole and the non-negative half-axis of the $x$-axis 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 $\rho^2 - 2\rho\cos\theta - 3 = 0$.
(1) If line $l$ has common points with curve $C$, find the range of values for the inclination angle $\alpha$;
(2) 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}
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