
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 game, the Swinging Hitters minor league baseball team offered the following incentives to its fans:
- Every 60th fan who entered the stadium received a coupon for a free hot dog.
- Every 40th fan who entered the stadium received a coupon for a free cup of soda.
- Every 90th fan who entered the stadium received a coupon for a free ice cream.

The stadium was expanded and now holds 5000 fans, which was completely full for this game. Determine how many fans received all three types of free items.

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