
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 table tennis competition rules, it is stipulated that in a game, before the score reaches 10-all, one side serves twice consecutively, then the other side serves twice consecutively, and so on. Each serve, the winning side scores 1 point, and the losing side scores 0 points. Assume in a match between player A and player B, the probability of the server scoring 1 point on each serve is 0.6, and the outcomes of each serve are independent. In a game where player A serves first:  
(Ⅰ) Calculate the probability that the score is 1 to 2 in favor of player B at the start of the fourth serve;  
(Ⅱ) Let $\xi$ represent the score of player B at the start of the fourth serve, calculate the expectation of $\xi$.

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