
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
In a certain junior high school, the seventh grade is preparing to watch the movie "Battle of Changjin Lake". Each class monitor is responsible for buying tickets, and the number of students in each class is more than 40. The ticket price is $30$ yuan per ticket. When a class monitor asked the ticket seller if group tickets could be discounted, the ticket seller said: for groups of 40 people or more, there are two discount options to choose from: Option 1: all members can get a $20\%$ discount; Option 2: if a $10\%$ discount is given, 5 people can get free tickets.<br/>$(1)$ If a certain class has 42 students, which option should they choose?<br/>$(2)$ After thinking for a while, a class monitor said, no matter which option they choose, the amount of money they have to pay is the same. Do you know how many students are in that class?

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