
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 line $C_1$ is given by $$y=- \sqrt {3}x$$, and the parametric equation of the curve $C_2$ is $$\begin{cases} x=- \sqrt {3}+\cos\phi \\ y=-2+\sin\phi \end{cases}$$ (where $\phi$ is the parameter). A polar coordinate system is established with the origin as the pole and the positive half-axis of $x$ as the polar axis.  
(Ⅰ) Find the polar equation of $C_1$ and the ordinary equation of $C_2$;  
(Ⅱ) Rotate $C_1$ clockwise around the origin by $\frac {\pi}{3}$ to get the line $C_3$. $C_3$ intersects $C_2$ at points A and B. Find $|AB|$.

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