
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 $C_1$ is $\rho=2\sin\theta$, and the parametric equation of curve $C_2$ is 
$$
\begin{cases} 
x=3+2t \\ 
y=t
\end{cases}
$$
(I) Convert the equations of curves $C_1$ and $C_2$ into Cartesian equations;  
(II) Take a point A on curve $C_1$ and a point B on curve $C_2$, find the minimum value of the length of segment AB.

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