
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
For the circle $C:x^2+y^2=r^2$, and points $A(6,0)$, $B(0,8)$, if point $P$ is any point on the line segment $AB$, and there always exist two points $M$, $N$ on the circle $C$ such that $\overrightarrow{PM}=\overrightarrow{MN}$, then the range of the radius $r$ is \_\_\_\_\_\_\_.

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