
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, curve C<sub>1</sub> is defined by the parametric equations $$\begin{cases} x= \frac { \sqrt {3}}{2}t \\ y= \frac {1}{2}t \end{cases}$$ (where $t$ is the parameter). In the polar coordinate system with the origin O as the pole and the positive x-axis as the polar axis, curve C<sub>2</sub> is given by $\rho=2\sin\theta$, and curve C<sub>3</sub> by $\rho=2\sqrt{3}\cos\theta$.
(Ⅰ) Find the polar equation of curve C<sub>1</sub>.
(Ⅱ) If curve C<sub>1</sub> intersects with curves C<sub>2</sub> and C<sub>3</sub> at points A and B (both different from the origin O), respectively, find the value of $|AB|$.

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