
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
Calvin estimates that there are 42,000 fans at a soccer game in Seattle, while Dana estimates that there are 55,000 fans at a soccer game in Denver. An official confirms that:
i. The actual attendance in Seattle differs from Calvin's estimate by at most $15\%$.
ii. Dana's estimate is within $8\%$ of the actual attendance in Denver.
Additionally, it is known that the actual total attendance in both games combined was around 95,000, give or take 1,000 fans.
What is the smallest possible difference between the numbers attending the two games, rounded to the nearest 100?
A) 3000
B) 4000
C) 5000
D) 6000
E) 7000

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