
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
It is known that there is 1 red ball and 2 black balls in box A, and 2 red balls and 2 black balls in box B, all of which are identical in shape and texture. Now, one ball is randomly drawn from each of the two boxes. Let $\xi$ be the number of red balls drawn out of the 2 balls, then the mathematical expectation $E\xi =$ ______.

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