
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 a circle with equation $(x-3)^2 + (y+5)^2 = r^2$ ($r > 0$), there are exactly two points on the circle at a distance of 1 from the line $4x - 3y - 2 = 0$. Find the range of the radius $r$ of this circle.

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