
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]


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At the beginning of the school year, $40\%$ of all students in Ms. Lee's class answered "Yes" to the question "Do you love science", and $60\%$ answered "No." At the end of the school year, $80\%$ answered "Yes" and $20\%$ answered "No." Altogether, $y\%$ of the students gave a different answer at the beginning and end of the school year. Find the difference between the maximum and the minimum possible values of $y$.

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