
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
The lottery now includes three drawings. First, a MegaBall is picked from among 30 numbered balls. Second, five WinnerBalls are picked from among 50 numbered balls. Third, a BonusBall is picked from among 15 numbered balls. To win the lottery, you must correctly pick the MegaBall number, the numbers on the five WinnerBalls (order does not matter for WinnerBalls), and the BonusBall. What is the probability that the ticket I hold has all the winning numbers?

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