
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 that line $l$ intersects with the parabola $y^2=4x$ at points $A$ and $B$, and is tangent to the circle $(x-4)^2+y^2=r^2$ ($r>0$) at point $M$, which is the midpoint of segment $AB$. If there are exactly 2 such lines $l$, find the set of possible values for $r$.

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