
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, a local sports team decides to give away promotional items to fans entering the stadium:
- Every 60th fan receives a free t-shirt.
- Every 45th fan receives a free hat.
- Every 75th fan receives a free keychain.
The stadium was filled to its capacity of 4500 fans for this event. How many fans received all three items?

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