
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 event, a local theater offers the following incentives to its guests:
- Every 90th guest receives a free movie ticket.
- Every 36th guest receives a free popcorn.
- Every 60th guest receives a free soda.
The theater can accommodate 3600 guests and was completely full for this event. How many of the guests were lucky enough to receive all three free items?

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