
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
Given $60\%$ of students like dancing and the rest dislike it, $80\%$ of those who like dancing say they like it and the rest say they dislike it, also $90\%$ of those who dislike dancing say they dislike it and the rest say they like it. Calculate the fraction of students who say they dislike dancing but actually like it.

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