
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 14 identical balls, including 7 red balls and 7 white balls. They are placed in two boxes, labeled A and B. Box A contains 4 red balls and 3 white balls, while box B contains 3 red balls and 4 white balls. One ball is randomly taken from box A and placed into box B, and then one ball is randomly taken from box B and placed back into box A. Let \(\xi\) denote the number of red balls in box B after these actions. Find the expected value \(E[\xi]\).

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