
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 equations of two circles are $x^2+y^2+6x-4=0$ and $x^2+y^2+6y-28=0$, and they intersect at points A and B,  
(1) Find the equation of the line where AB lies.  
(2) Find the length of the common chord AB of the two circles.

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