
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 rectangular coordinate system, the parametric equation of line $l$ is $$\begin{cases} x=t\cos\alpha \\ y=t\sin\alpha \end{cases}$$ ($t$ is the parameter, $0≤α<π$). Establish a polar coordinate system with the coordinate origin as the pole and the positive semi-axis of the $x$-axis as the polar axis. The polar equation of curve $C$ is $ρ^2-4=4ρ\cosθ-2ρ\sinθ$.

(I) Write the rectangular coordinate equation of curve $C$;

(II) If line $l$ intersects curve $C$ at points $A$ and $B$, and the length of $AB$ is $2\sqrt{5}$, find the general equation of line $l$.

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