
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 $xOy$, there is a line $l$ given by the parametric equations $\begin{cases} x=t \\ y=- \sqrt {3}t \end{cases}$ (where $t$ is a parameter), and a curve $C_1$ given by the parametric equations $\begin{cases} x=\cos\theta \\ y=1+\sin\theta \end{cases}$ (where $\theta$ is a parameter). Taking the origin $O$ of this Cartesian coordinate system as the pole and the non-negative half-axis of $x$ as the polar axis, the equation of the curve $C_2$ in the polar coordinate system is $\rho=-2\cos\theta+2\sqrt {3}\sin\theta$.  
(1) Find the polar coordinate equation of curve $C_1$ and the Cartesian coordinate equation of curve $C_2$;  
(2) Suppose the line $l$ intersects curve $C_1$ at points $O$ and $A$, and intersects curve $C_2$ at points $O$ and $B$, find the length of $|AB|$.

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