
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 an extended game, each of 6 players, including Hugo, rolls a standard 8-sided die. The winner is the one who rolls the highest number. In the case of a tie for the highest roll, the tied players will re-roll until a single winner emerges. What is the probability that Hugo's first roll was a 7, given that he won the game?
A) $\frac{2772}{8192}$
B) $\frac{8856}{32768}$
C) $\frac{16056}{65536}$
D) $\frac{11028}{49152}$
E) $\frac{4428}{16384}$

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