
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 O as the pole and the positive x-axis as the polar axis, a polar coordinate system is established. The polar equations of circle $C_1$ and line $C_2$ are $\rho=4\sin\theta$ and $\rho\cos(\theta- \frac{\pi}{4})=2\sqrt{2}$, respectively.  
(1) Find the Cartesian equations of circle $C_1$ and line $C_2$.  
(2) Find the polar coordinates of the intersection points of circle $C_1$ and line $C_2$.

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