
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
Li Lei and Han Meimei are playing a game of Go. They agreed that the winner of each round gets 1 point, while the loser gets 0 points. The game stops when one player is ahead by 2 points or after 4 rounds have been played. It is given that the probability of Li Lei winning a round is $P(P>\frac{1}{2})$, and the outcomes of each round are independent. It is known that the probability of the game ending after the second round is $\frac{5}{8}$. Find the value of the probability $P$.

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