
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
Selected Exercise $4-4$: Coordinate Systems and Parametric Equations

In the rectangular coordinate system $xOy$, the parametric equations of the curve $C_{1}$ are given by $\begin{cases} x=-t \\ y=-1+\sqrt{3}t \end{cases}$ (where $t$ is the parameter). A polar coordinate system is established with the coordinate origin as the pole and the positive $x$-axis as the polar axis. The polar equation of the curve $C_{2}$ is $\rho = 2\sin \theta - 2\sqrt{3}\cos \theta$.

(I) Find the ordinary equation of the curve $C_{1}$ and the rectangular coordinate equation of the curve $C_{2}$;

(II) If the curves $C_{1}$ and $C_{2}$ intersect at points $A$ and $B$, find $|AB|$.

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