
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
Estimates suggest that Charles attends a baseball game in Chicago, estimating 80,000 fans, and Dale attends a game in Detroit with an estimate of 95,000 fans. A league official notes that:
i. The actual attendance in Chicago is within $5\%$ of Charles' estimate.
ii. The actual attendance in Detroit is within $15\%$ of Dale's estimate.
Determine, to the nearest 1,000, the largest possible difference between the numbers attending the two games.
A) 32000
B) 34000
C) 36000
D) 38000
E) 40000

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