
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
Mr. QQ has a fish tank with 7 fish, including 6 blue fish and 1 black fish. Starting from today, he plans to catch and eat 1 fish from the tank every noon (each fish has an equal probability of being caught). If the black fish is not caught, it will eat 1 blue fish every night (it is assumed that blue fish do not eat fish).
(1) Calculate the probability that at least 5 of these 7 fish are eaten by Mr. QQ;
(2) Let $\xi$ represent the number of fish eaten by Mr. QQ out of these 7 fish, calculate $E\xi$.

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