
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 rectangular coordinate system $(xOy)$, the equation of circle $C$ is $((x-1)^{2}+(y-2)^{2}=1)$. Establish a polar coordinate system with the origin $O$ as the pole and the positive semi-axis of $x$ as the polar axis.
(1) Find the polar coordinate equation of circle $C$;
(2) If the parameter equation of line $l$ is $= \begin{cases} x=1+ \frac { \sqrt {3}}{2}t \\ y= \frac {1}{2}t\end{cases}(t$ is the parameter$)$, find the range of distances from points on circle $C$ to line $l$.

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