
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 special event held at a theater, the management decided to give away free gifts based on seat number arrangements:
- Every 45th attendee received a free poster.
- Every 75th attendee received a free program.
- Every 100th attendee received a free keychain.

The theater was fully occupied, holding a maximum of 4500 attendees. Determine how many attendees received all three items.

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