
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 chess competition, the rules are as follows: when two players compete, the winner of each game scores 1 point, and the loser scores 0 points. The competition stops when one player scores 3 more points than the other, or when 7 games have been played (it is possible that there is no winner). Suppose in a match between player A and player B from a certain school, the probability of A winning each game is $p$ ($p > \frac{1}{2}$), and the outcomes of the games are independent of each other. It is known that the probability of the match stopping after the third game is $\frac{1}{3}$. The probability of A winning is \_\_\_\_\_\_.

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