
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 between players A and B, it is assumed that the probability of A winning each game is $\frac{2}{3}$ and the probability of B winning is $\frac{1}{3}$. There is no possibility of a draw.
(1) If the two play 3 games, find the probability that A wins exactly 2 games and the probability that B wins at least 1 game;
(2) If the match is based on a best-of-five format (meaning that the match ends when either A or B wins 3 games first, and the winner is the one who reaches 3 wins first), find the probability that A wins.

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