
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
Given the polar equation of curve $C$ is $\rho=2\cos \theta-4\sin \theta$, with the pole as the origin and the polar axis as the positive half-axis of $x$, establish a Cartesian coordinate system. The parametric equation of line $l$ is $\begin{cases} & x=1+t\cos \alpha \\ & y=-1+t\sin \alpha \\ \end{cases}$ (where $t$ is the parameter).

(Ⅰ) Determine the positional relationship between line $l$ and curve $C$, and explain the reason;

(Ⅱ) If line $l$ intersects curve $C$ at points $A$ and $B$, and $|AB|=3\sqrt{2}$, find the slope of line $l$.

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