
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
The graph of an equation \[\sqrt{(x-6)^2 + (y+3)^2} + \sqrt{(x+4)^2 + (y-5)^2} = 24.\] describes a geometric shape. What is the distance between its foci if it is given that the center of the shape is the midpoint between the foci?

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