
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 where the winner is the first to secure 3 sets, with the match concluding immediately upon reaching this victory condition. It is given that Team A has a probability of winning the fifth set at $\frac{1}{2}$, whereas for all the other sets, their probability of winning is $\frac{2}{3}$. Assuming the outcomes of the sets are independent, the probability of Team A securing victory in the match is ______.

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