
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 two circles $C_{1} : x^{2} + y^{2} = 4$ and $C_{2} : (x - 1)^{2} + (y - 2)^{2} = r^{2} (r > 0)$, find the range of $r$ when circles $C_{1}$ and $C_{2}$ have exactly two common tangent lines.

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