
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 basketball game event, the Dunking Giants team offered these incentives to its fans:

Every 100th fan who entered the arena received a free T-shirt.

Every 45th fan who entered the arena received a free baseball cap.

Every 60th fan who entered the arena received a free pair of socks.

The arena holds 5000 fans and was filled to capacity for this game. How many of the fans at the game received all three items?

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