
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 a local baseball game, the following offers are made to the attending fans:

Every 90th fan who entered the stadium received a coupon for a free hot dog.

Every 45th fan who entered the stadium received a coupon for a free cup of soda.

Every 60th fan who entered the stadium received a coupon for a free bag of popcorn.

Every 45th fan also received a free ice cream.

The stadium was sold out with a capacity of 4500 fans. How many fans received all four offers?

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