
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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In a special promotional event for a hockey game, every 60th fan received a free soda voucher, every 80th fan received a free popcorn voucher, and every 100th fan received a free hot dog voucher. The arena was sold out with a total capacity of 4500 fans. Determine how many fans received all three items.

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