
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 store, there are 50 light bulbs in stock, 60% of which are produced by Factory A and 40% by Factory B. The first-class rate of the light bulbs produced by Factory A is 90%, and the first-class rate of the light bulbs produced by Factory B is 80%.

(1) If one light bulb is randomly selected from these 50 light bulbs (each light bulb has an equal chance of being selected), what is the probability that it is a first-class product produced by Factory A?

(2) If two light bulbs are randomly selected from these 50 light bulbs (each light bulb has an equal chance of being selected), and the number of first-class products produced by Factory A among these two light bulbs is denoted as $\xi$, find the value of $E(\xi)$.

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