
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 Chloe's estimate of 40,000 is within $5\%$ of the actual attendance in Chicago, Derek's estimate of 55,000 is within $15\%$ of the actual attendance in Denver, and Emma's prediction of 75,000 is within $10\%$ of the actual count in Miami, calculate the largest possible difference between the numbers attending any two of these three events to the nearest 1,000.

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