
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
In a match without draws, the competition ends when one person wins 2 more games than the other, and the person with more wins is the winner. It is known that in odd-numbered games, the probability that player A wins is $\frac{3}{5}$, and in even-numbered games, the probability that player B wins is $\frac{3}{5}$. Find the expected number of games played when the match ends.

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