
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 choice between coordinate system and parametric equations) In the Cartesian coordinate system, the parametric equation of circle C is $$\begin{cases} \left.\begin{matrix}x=2\cos\theta \\ y=2+2\sin\theta\end{matrix}\right.\end{cases}$$ ($\theta$ is the parameter). Then, the standard equation of circle C is \_\_\_\_\_\_, and establishing a polar coordinate system with the origin O as the pole and the positive x-axis as the polar axis, the polar coordinates of the center of circle C are \_\_\_\_\_\_.

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