
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
Athletes were surveyed using Warner's random response technique, where respondents answered one of two questions depending on the roll of a die. If an odd number was rolled, they answered the first question; if an even number was rolled, they answered the second question. This resulted in 54 "yes" responses out of 200 surveyed athletes. Estimate the proportion of people who have used performance-enhancing drugs among this group.

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