
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
Two circles, each of radius $4$, are placed with centers at $(0, 12)$ and $(6, 10)$. A line passing through $(4,0)$ needs to be found such that it equally divides the total area of both circles. What is the absolute value of the slope of this line?

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