
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
For a special sports event, the Slam Dunk Basketball team decided to run a promotional campaign with the following offers:

Every 45th fan at the entrance received a free t-shirt.
Every 50th fan received a free basketball.
Every 100th fan received a free pair of sneakers.

The arena has a capacity of 5000 persons and it was completely full. Determine how many fans received all three promotional items.

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