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

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