
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
From a batch of products, a product is drawn twice with replacement, each time randomly drawing 1 piece. Assume event A: "At most one of the two drawn products is of second quality" has a probability $P(A) = 0.96$.  
(1) Find the probability $p$ that any one piece drawn from this batch is of second quality;  
(2) If there are 100 pieces in this batch, and 2 pieces are randomly drawn, find the probability of event B: "At least one of the two drawn products is of second quality".

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