
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 the start of the semester, $60\%$ of the students in Ms. Rose's class preferred studying history, and $40\%$ preferred geography. At the end of the semester, $80\%$ preferred history and $20\%$ preferred geography. Calculate the percentage $y\%$ of students who changed their preference during the semester. What is the difference between the maximum and the minimum possible values of $y$?
A) 10%
B) 20%
C) 30%
D) 40%
E) 50%

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