
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 parametric equations of curve $C_1$ as $$\begin{cases} x=4+5\cos t \\ y=5+5\sin t \end{cases}$$ (where $t$ is the parameter), and establishing a polar coordinate system with the origin as the pole and the positive half-axis of $x$ as the polar axis, the polar equation of curve $C_2$ is $\rho=2\sin\theta$.  
(1) Convert the equations of $C_1$ and $C_2$ into Cartesian equations;  
(2) Find the polar coordinates of the intersection points of $C_1$ and $C_2$ ($\rho>0$, $0\leq\theta<2\pi$).

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