
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 dice game, each of 5 players, including Hugo, rolls a standard 6-sided die. The winner is the player who rolls the highest number. In the event of a tie for the highest roll, those involved in the tie roll again until a clear winner emerges. What is the probability that Hugo's first roll was a 6, given that he won the game and his roll was at least 4?
A) $\frac{625}{4626}$
B) $\frac{5}{24}$
C) $\frac{1}{6}$
D) $\frac{625}{7776}$
E) $\frac{625}{1296}$

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