
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 that Charlie estimates 80,000 fans in Chicago, Daisy estimates 70,000 fans in Denver, and Ed estimates 65,000 fans in Edmonton, and given the actual attendance in Chicago is within $12\%$ of Charlie's estimate, Daisy's estimate is within $15\%$ of the actual attendance in Denver, and the actual attendance in Edmonton is exactly as Ed estimated, find the largest possible difference between the numbers attending any two of the three games, to the nearest 1,000.

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