
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 points A(-2, 0), B(2, 0), and a point P on the circle $(x-3)^2+(y-4)^2=r^2$ ($r>0$), satisfying $PA^2+PB^2=40$. If there are two such points P, then the range of values for $r$ is ______.

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