
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 special game night of the Pioneers collegiate basketball team, the following offers were made to fans:

- Every 100th fan got a free coffee.
- Every 40th fan received a free water bottle.
- Every 60th fan received a free T-shirt.
- Every 24th fan received a free hat.

The arena was packed with 7200 fans for this game. How many fans received all four items?

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