
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 甲 and 乙 play a ping pong match, where each match winner gets $1$ point and loser gets $0$ point, and the match stops when one player leads the other by $2$ points or after $6$ matches. If 甲 wins each match with a probability of $\dfrac{2}{3}$ and 乙 wins each match with a probability of $\dfrac{1}{3}$, and the outcomes of each match are independent, determine the expected number of matches $\xi$ when the match stops.

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