
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 as the pole and the positive half-axis of $x$ as the polar axis, a polar coordinate system is established. For curve $C$: $\rho= \frac {3}{2-\cos\theta }$, $\theta\in[0,2\pi)$, and line $l$ $\begin{cases} x=3+t \\ y=2+2t \end{cases}$ (where $t$ is a parameter, $t\in\mathbb{R}$)  
(1) Find the general equations of curve $C$ and line $l$.  
(2) Suppose line $l$ intersects curve $C$ at points $A$ and $B$, find the value of $|AB|$.

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