
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
Carmen attends a baseball game in Chicago and estimates that there are 70,000 fans in attendance. Dave attends a baseball game in Denver and estimates that there are 85,000 fans in attendance. A league official who knows the actual numbers attending the two games notes that:
i. The actual attendance in Chicago is within $8\%$ of Carmen's estimate.
ii. Dave's estimate is within $12\%$ of the actual attendance in Denver.
To the nearest 1,000, the largest possible difference between the numbers attending the two games is:
(__)
A) 28000
B) 30000
C) 32000
D) 34000

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