
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
There are two teams competing in a match, with each team having a probability of $\frac{1}{2}$ to win each game. It is stipulated that a team must win four consecutive games to end the match. The number of games played is a random variable $\xi$. What is the expected value $E(\xi)$ of $\xi$?

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