
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]


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Given Charlie and Dana's estimates of the fans in attendance at the Cincinnati and Denver games are 70,000 and 80,000, respectively. Additionally, the actual attendance in Cincinnati is within 15% of Charlie’s estimate and Dana’s estimate is within 15% of the actual attendance in Denver. Determine the largest and smallest possible difference between the numbers attending the two games.

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