
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
The common chord length of the two circles $x^2+y^2+4x-4y=0$ and $x^2+y^2+2x-12=0$ can be calculated by finding the distance between their centers minus the radii of the circles. Find the distance between the centers of these two circles.

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