
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
Let set $A=\{(x,y) | x^2+y^2=4\}$, and set $B=\{(x,y) | (x-3)^2+(y-4)^2=r^2\}$, where $r>0$. If $A \cap B$ contains exactly one element, then the value of $r$ is $\_\_$ $\_\_\_\_$.

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