
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
Find the positive value for the slope of an asymptote of the hyperbola defined by:
\[
\sqrt{(x-1)^2+(y+1)^2} - \sqrt{(x-7)^2+(y+1)^2} = 4
\]

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