
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 the game of Avalon, there are  $10$  players,  $4$  of which are bad. A *quest* is a subset of those players. A quest fails if it contains at least one bad player. A randomly chosen quest of  $3$  players happens to fail. What is the probability that there is exactly one bad player in the failed quest?

*2018 CCA Math Bonanza Team Round #3*

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