
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 game, each of 5 players rolls a standard 6-sided die. The winner is the player who rolls the highest number. If there is a tie for the highest roll, those involved must roll again. This continues until only one person has the highest number. If Cecilia is one of the players, what is the probability that Cecilia's first roll was a 4, given that she won the game?
A) $\frac{41}{144}$
B) $\frac{256}{1555}$
C) $\frac{128}{1296}$
D) $\frac{61}{216}$

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