
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
Players A and B play badminton, playing three consecutive games, with the results of each game being independent of each other. If the probability of player A winning in the first, second, and third games is $\frac{1}{4}$, $\frac{1}{3}$, and $\frac{1}{3}$ respectively, determine the probability of player A winning exactly two consecutive games.

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