
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
There are 5 ping pong balls, among which 3 are new and 2 are old (i.e., used at least once). Each time a match occurs, 2 balls are selected and used, and then all balls are returned. Let $\xi$ be the number of new balls picked in the second match. What is the expected value $E(\xi)$?

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