
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 parametric equation of line $l$ is 
$$
\begin{cases} 
x = t\cos\alpha \\
y = 1 + t\sin\alpha 
\end{cases}
$$
($t$ is the parameter). In the polar coordinate system with the origin $O$ as the pole and the positive half-axis of $x$ as the polar axis, the polar equation of curve $C$ is $\rho\cos^2\theta = 4\sin\theta$.  
(1) Let $M(x, y)$ be any point on curve $C$, find the range of values for $x+y$;  
(2) If line $l$ intersects curve $C$ at points $A$ and $B$, find the minimum value of $|AB|$.

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