
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
When and only when $m \leq r \leq n$, the two circles $x^2+y^2=49$ and $x^2+y^2-6x-8y+25-r^2=0$ ($r>0$) have common points, then the value of $n-m$ is ______.

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