
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
A lottery game consists of two main draws and a bonus draw. Initially, a BonusBall is picked from 15 numbered balls. Next, a MegaBall is picked from 30 numbered balls. Finally, six WinnerBalls are picked from 50 numbered balls. To win the lottery, you must correctly pick the MegaBall number and the numbers on the six WinnerBalls. You also need to guess the BonusBall which, if correct, doubles your chances of winning the lottery since it allows two opportunities for guess sets on WinnerBalls. What is the probability that the ticket I hold has the winning numbers assuming the BonusBall is guessed correctly?

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