
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
Teams A and B are playing a volleyball match. The first team to win 3 sets will be declared the winner, and the match will end immediately. Except for the fifth set, where Team A has a probability of $\frac{1}{2}$ to win, Team A has a probability of $\frac{2}{3}$ to win in all other sets. Assume that the results of each set are independent. The probability that Team A will win is _______.

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