
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 lottery game, there are two drawings. First, a MegaBall is picked from among 30 numbered balls. Second, five WinnerBalls are picked from among 50 numbered balls. To win the lottery, you must correctly guess the number on the MegaBall and the numbers on the five WinnerBalls (order does not matter for the WinnerBalls). What is the probability that the ticket I hold contains the winning numbers?

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