
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
Assume in a market, products from Factory A account for $60\%$, products from Factory B account for $40\%$. The qualification rate of Factory A products is $90\%$, and the qualification rate of Factory B products is $80\%$. If two light bulbs from Factory A are purchased in this market, the probability that exactly one of them is qualified is ____; if a light bulb is randomly purchased in this market, the probability that it is qualified is ____.

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