
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 bag, there are 10 cards of the same size but different colors, including 5 red cards, 3 white cards, and 2 blue cards. A card is randomly drawn from the bag, its color is determined, and then it is put back into the bag. If a white card is drawn, no more cards are drawn. Otherwise, continue drawing cards, but no more than 3 times in total.
- (I) Let event $A$ be "exactly 2 red cards are drawn". Find $P(A)$.
- (II) Let the random variable $\xi$ represent the number of cards drawn. Find the probability distribution and the expected value $E(\xi)$ of the random variable $\xi$.

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