
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
Given a computer program generates a random five-digit binary number $A=a_1a_2a_3a_4a_5$, where for $A$, $a_1=1$, and for $a_k$ ($k=2, 3, 4, 5$), the probability of being $0$ is $\frac{1}{3}$, and the probability of being $1$ is $\frac{2}{3}$. Let $\xi = a_1 + a_2 + a_3 + a_4 + a_5$. Calculate the expected value of $\xi$.

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