
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]


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Given the parametric equation of line $l$ as $$\begin{cases} x=1+t \\ y= \sqrt {3}+ \sqrt {3}t \end{cases}$$ (where $t$ is the parameter). In the polar coordinate system with the origin $O$ as the pole and the non-negative half-axis of the $x$-axis as the polar axis, the polar equation of curve $C$ is $\rho^2-4\rho\cos\theta-2\sqrt{3}\rho\sin\theta+4=0$.

(Ⅰ) Find the standard equation of line $l$ and the Cartesian coordinate equation of curve $C$;  
(Ⅱ) Suppose line $l$ intersects curve $C$ at points $A$ and $B$, calculate $|OA|\cdot|OB|$.

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