
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
Three circles, each of radius 4, are drawn with centers at $(10, 90)$, $(15, 80)$, and $(20, 85)$. A line passing through $(15,80)$ needs to be found such that the total area of the parts of the three circles to one side of the line equals the total area of the parts of the three circles to the other side of it. What is the absolute value of the slope of this line?

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