
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
During the New Year's Day period, a class organized a visit to the Jiangbei City Science Museum and the Opera House. Below is a record of a conversation between the class teacher and the travel agency:  
Class teacher: How much is the charge per person for a group visit to the Chongqing Science Museum and Opera House?  
Tour guide: Hello! If the number of people does not exceed 30, the charge is 100 yuan per person (including tickets).  
Class teacher: How about a discount for more than 30 people?  
Tour guide: If it exceeds 30 people, for every additional person, the per capita cost decreases by 2 yuan, but the per capita cost cannot be lower than 72 yuan.  
After organizing the visit according to this charging standard, the class paid a total of 3150 yuan to the travel agency. Based on the above scenario, could you help the class teacher count the number of people in the class who visited this time?

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