
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 revised lottery, a MegaBall is selected from 30 numbered balls. Then, seven WinnerBalls are drawn from 50 numbered balls. To win the jackpot, a ticket must correctly guess the MegaBall and the numbers on all seven WinnerBalls. Additionally, to win a special bonus prize, the first two WinnerBalls must be guessed in the exact order they are drawn, while the remaining five can be in any order. What is the probability that the ticket I hold will win the jackpot and the special bonus prize?

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