
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, with the origin O as the pole and the positive half-axis of the x-axis as the polar axis, the polar coordinate system is established. Given that the line $\begin{cases} \left.\begin{matrix}x=-t \\ y= \sqrt {3}t\end{matrix}\right.\end{cases}$ (where $t$ is a parameter) intersects the curve $C_1: \rho=4\sin\theta$ at a point A other than O, and intersects the curve $C_2: \rho=2\sin\theta$ at a point B other than O, find the length of |AB|.

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