
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 $\begin{cases} x=t\cos \alpha \\ y=1+t\sin \alpha \end{cases}$ (where $t$ is the parameter, $\alpha\in[0,\pi)$). 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 $xOy$. Suppose the polar equation of curve $C$ is $\rho\cos^2\theta=4\sin\theta$.
- (Ⅰ) Let $M(x,y)$ be any point on curve $C$, find the range of values for $x+y$;
- (Ⅱ) If line $l$ intersects curve $C$ at two points $A$ and $B$, find the minimum value of $|AB|$.

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