
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 the market, the supply of light bulbs from Factory A accounts for 70%, while those from Factory B account for 30%. The pass rate for Factory A's products is 95%, and for Factory B's products, it is 80%. Let event A denote the selection of a light bulb from Factory A and event $\overline{A}$ denote the selection from Factory B. B indicates the event that the selected light bulb passes the quality test.

(1) Write down the probabilities associated with these events;  
(2) Calculate the probability of purchasing a qualified light bulb produced by Factory A from the market.

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