
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 equation of the curve $C_1$ as 
$$
\begin{cases} 
x=4+5\cos t, \\ 
y=5+5\sin t 
\end{cases}
(t \text{ is the parameter}),
$$
and establishing a polar coordinate system with the origin as the pole and the positive x-axis as the polar axis, the polar equation of the curve $C_2$ is $\rho =2\sin \theta$.

(I) Convert the parametric equation of $C_1$ into a polar equation;

(II) Find the polar coordinates of the intersection points between $C_1$ and $C_2$ ($\rho \geqslant 0,0\leqslant \theta < 2\pi$).

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