
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
In a certain study on health risk factors denoted by X, Y, and Z within a group of 200 people, the probability that a person has only one of these risk factors is 0.07 for each. The probability that a person has exactly two out of the three risk factors is 0.12 for any two factors. The probability that a person has all three risk factors, given that they have X and Y, is 0.4. What is the probability that a person has none of the risk factors given they don't have risk factor X?

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