
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 line $l$ intersect the parabola $x^2=4y$ at points $A$ and $B$, and be tangent to the circle $x^2+(y-5)^2=r^2$ ($r>0$) at point $M$, with $M$ being the midpoint of segment $AB$. If there are exactly 4 such lines $l$, determine the range of the real number $r$.

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