
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
Red team members A, B, and C play Go with blue team members $A$, $B$, $C$. A plays against $A$, B plays against $B$, and C plays against $C$, with the probabilities of A winning against $A$, B winning against $B$, and C winning against $C$ being $0.6$, $0.5$, and $0.5$ respectively. Assume the results of each match are independent.<br/>$(1)$ Find the probability that at least two members of the red team win is ______;<br/>$(2)$ Let $ \xi $ represent the total number of wins by the red team members. Find the expected value of $\xi$.

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