
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 three circles, each with a radius of 3, and centers at \((14, 92)\), \((17, 76)\), and \((19, 84)\), find the absolute value of the slope of a line passing through the point \((17, 76)\) such that the sum of the areas of the parts of the circles on one side of the line is equal to the sum of the areas of the parts of the circles on the other side of the line.

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