
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
Two students, A and B, are preparing to have a table tennis match during their physical education class. Assuming that the probability of A winning against B in each game is $\frac{1}{3}$, the match follows a best-of-three format (the first player to win two games wins the match). What is the probability of A winning the match?

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