
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 circle C with the equation $$\begin{cases} x=1+\cos\theta \\ y=1+\sin\theta \end{cases}$$ (where $\theta$ is the parameter), establish a polar coordinate system with the origin O as the pole and the positive x-axis as the polar axis. Find the polar coordinates of the center of the circle C. (The range of the polar angle is $[0, 2\pi)$).

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