
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 curve $C_1$ with the polar equation $\rho=4\sin \theta$, and a Cartesian coordinate system with the pole as the origin and the polar axis as the positive $x$-axis direction, the curve $C_2$ has the parametric equation \[\begin{cases} x= \dfrac{1}{\sqrt{2}}(t+ \dfrac{1}{t}) \\ y= \dfrac{1}{\sqrt{2}}(t- \dfrac{1}{t})\end{cases}\ (t\text{ is the parameter}).\]  
(I) Convert the parametric equation of $C_2$ into a Cartesian equation;  
(II) Find the polar coordinates of the points where $C_1$ and $C_2$ intersect.

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