
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 $xoy$, point $P$ is a moving point on the line $3x+4y+3=0$. Two tangents are drawn from point $P$ to the circle $C: x^2+y^2-2x-2y+1=0$, and the points of tangency are $A$ and $B$, respectively. The range of values for $|AB|$ is \_\_\_\_\_\_.

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