
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 event, the Clever Cats basketball team provided the following incentives to its fans:
- Every 90th fan who entered the stadium received a coupon for a free beverage.
- Every 45th fan who entered the stadium received a coupon for a free snack.
- Every 60th fan who entered the stadium received a coupon for a free hat.
- Every 100th fan who entered the stadium received a free t-shirt.
The stadium holds 5000 fans and was completely full for this event. How many of the fans at the event were fortunate enough to receive all four free items?

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