
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 with a radius of $4$ units, have centers at $(0, 20)$ and $(7, 13)$. A line passing through the point $(4, 0)$ needs to be drawn such that the total area of the parts of both circles on one side of the line is equal to the total area of the parts of both circles on the other side of the line. What is the absolute value of the slope of this line?

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