
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
A new math teacher joined a class and conducted a survey among the students regarding their liking for mathematics. It turned out that $50\%$ of the students liked mathematics and $50\%$ did not. The same survey was conducted at the end of the school year. This time, $60\%$ of the students answered "yes" and $40\%$ answered "no". Let $x\%$ of the students have given a different answer in the second survey compared to the first. Find the minimum and maximum value of $x$.

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