
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 given by $$\begin{cases} x=t\cos\alpha \\ y=t\sin\alpha \end{cases}$$ ($t$ is the parameter), and a polar coordinate system is established with the origin $O$ as the pole and the non-negative semi-axis of the $x$-axis as the polar axis. The polar equation of curve $C$ is $\rho^2-4\rho\cos\theta+3=0$.

(I) Find the general equation of line $l$ and the Cartesian equation of curve $C$.
(II) Suppose line $l$ intersects curve $C$ at points $A$ and $B$. When $\alpha\in(0, \frac{\pi}{6})$, find the range of $|OA|+|OB|$.

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