
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 players, A and B, take turns shooting baskets. The probability of A making a basket on each shot is $\frac{1}{2}$, while the probability of B making a basket is $\frac{1}{3}$. The rules are as follows: A goes first, and if A makes a basket, A continues to shoot; otherwise, B shoots. If B makes a basket, B continues to shoot; otherwise, A shoots. They continue to shoot according to these rules. What is the probability that the fifth shot is taken by player A?

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