
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
 
1. At Cornthwaite High School, many students enroll in an after-school arts program. The program offers a drama class and a music class. Each student enrolled in the program is in one class or both classes.

(a) This year, 41 students are in the drama class and 28 students are in the music class. If 15 students are in both classes, how many students are enrolled in the program?

(b) In 2014, a total of 80 students enrolled in the program. If \(3x - 5\) students were in the drama class, \(6x + 13\) students were in the music class, and \(x\) students were in both classes, determine the value of \(x\).

(c) In 2013, half of the students in the drama class were in both classes and one quarter of the students in the music class were in both classes. A total of \(N\) students enrolled in the program in 2013. If \(N\) is between 91 and 99, inclusive, determine the value of \(N\).

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