
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 a Cartesian coordinate system, the parametric equation of circle C is given by
$$
\begin{cases}
x=2\cos\theta \\
y=2+2\sin\theta
\end{cases}
$$
where $\theta$ is the parameter. Establishing a polar coordinate system with the origin as the pole and the positive x-axis as the polar axis, find the polar coordinates of the center of circle C.

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