
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
Larry and Julius are once more playing their turn-based game, throwing a ball at a bottle on a ledge. However, this time, there are changes in their accuracy. Suppose the probability Larry knocks off the bottle is $\tfrac{2}{3}$ each time it's his turn, and Julius has a probability of $\tfrac{1}{3}$. Larry still throws first. What is the probability that Larry wins the game under these new conditions?
A) $\dfrac{5}{7}$  
B) $\dfrac{6}{7}$  
C) $\dfrac{10}{14}$  
D) $\dfrac{12}{15}$

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