
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 that 50% of the students at Central College like dancing, and those who like dancing have a 30% false negative rate, with the remaining 70% accurately expressing their liking, and those who dislike dancing have an 20% false positive rate, with the remaining 80% accurately expressing their dislike, find the fraction of students who say they dislike dancing who actually like dancing.

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