
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
Athletes A and B, two table tennis players, are playing a badminton singles match. Based on their past match results, it is known that the probability of A winning a game is $0.6$, and the probability of B winning a game is $0.4$. If the match follows the "best of three" format (the first player to win two games wins), then if A wins the first game, the probability of A winning the match is ______.

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