
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 Cartesian coordinate system $xOy$, if there exists a point $P$ on the circle $C_1$: $x^2+(y-1)^2=r^2$ $(r > 0)$, and the symmetric point $Q$ of point $P$ with respect to the line $x-y=0$ lies on the circle $C_2$: $(x-2)^2+(y-1)^2=1$, then the range of values for $r$ is __________.

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