
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 the opening ceremony of a football game, the local team offered the following incentives to its fans:

Every 60th fan who entered the stadium got a free scarf.

Every 45th fan who entered the stadium got a free cap.

Every 75th fan who entered the stadium got a free flag.

The stadium holds 4500 fans and was completely full for this game. How many of the fans at the game were lucky enough to receive all three free items?

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