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

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