
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
Given the polar equation of curve $C$ is $\rho=4\sin \theta$. If we establish a Cartesian coordinate system with the pole as the origin and the positive half-axis of the polar axis as the $x$-axis, and the parametric equation of line $l$ is $\begin{cases} x=2\cdot t \\ y= \sqrt {3}\cdot t+2\end{cases}$ (where $t$ is the parameter), then the length of the segment cut off by curve $C$ on line $l$ is ______.

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