
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 there are 200 students in total, 75% of them are interested in art, and the rest are not. Of those students who are interested in art, 70% accurately say they like it and the remaining 30% say they dislike it. Among those who are not interested in art, 80% correctly state they dislike it, and 20% claim they like it. Determine the fraction of the students who claim they dislike art that are genuinely interested in it.

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