
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, the parametric equation of line $l$ is $\begin{cases} & x=t \\ & y=2t \end{cases}$ (where $t$ is the parameter), with the origin as the pole and the positive half-axis of $x$ as the polar axis, a polar coordinate system is established. It is known that the polar equation of curve $C$ is $\rho^{2}+2\rho\sin \theta-3=0$.

$(I)$ Find the polar equation of line $l$;

$(II)$ If line $l$ intersects curve $C$ at points $A$ and $B$, find $|AB|$.

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