
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 the center of circle C lies on the line x+y-8=0, and circle C is tangent to both lines l<sub>1</sub>: y=2x-21 and l<sub>2</sub>: y=2x-11.
(1) Find the equation of circle C.
(2) If line l: 2x+ay+6a=ax+14 intersects circle C at two distinct points M and N, find the minimum length of MN.

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