
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
In a modified dice game, 5 players each roll a standard 6-sided die. A player wins if they roll the highest number. In case of a tie, the tied players, except the previous round winner, roll again until there is a clear winner. Hugo is one of the players. Calculate the probability that Hugo's first roll was a 4, given that he won the game.
A) $\frac{71}{1296}$  
B) $\frac{367}{1296}$  
C) $\frac{1}{6} \times \Psi$   
D) $\frac{185}{648}$  
E) $\frac{11}{36}$

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