
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 the line $l$ intersects the parabola $y^2=6x$ at points $A$ and $B$, and the circle $(x-6)^2+y^2=r^2$ is tangent to the line $l$ at point $M$, which is the midpoint of segment $AB$. If there are exactly 4 such lines $l$, determine the range of values for $r$.

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