
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
Amanda attends a baseball game in Atlanta and estimates that there are 55,000 fans in attendance. Blake attends a baseball game in Boston and estimates that there are 58,000 fans in attendance. A league official, knowing the actual numbers, states:
i. The actual attendance in Atlanta is within $15\%$ of Amanda's estimate.
ii. The actual attendance in Boston is within $10\%$ of Blake's estimate.
To the nearest 1,000, the largest possible difference between the numbers attending the two games is:
A) 16000
B) 17000
C) 18000
D) 19000
E) 20000

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