
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, Julius, and Maria are playing a sequential game where they take turns throwing a ball at a bottle on a ledge. Larry goes first, then Julius, followed by Maria, and the sequence repeats in this order. The winner is the first person to successfully knock the bottle off the ledge with two consecutive hits. At each turn, the probability that a player knocks the bottle off the ledge is exactly $\tfrac{1}{3}$. Find the probability that Larry is the first to win.

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