
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
At the season opener, the Super Sluggers baseball team rolled out these promotions for fans:

- Every 90th fan receives a free baseball cap.
- Every 45th fan receives a free T-shirt.
- Every 60th fan receives a free pair of sunglasses.

The stadium, with a capacity of 4500, was filled to the brim. Determine how many fans received all three promotional items.

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