
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 system, there are three drawings:
1. A MegaBall is picked from among 30 numbered balls.
2. Five WinnerBalls are picked from among 50 numbered balls.
3. One SpecialBall is picked from the remaining 45 balls (after the WinnerBalls are selected).
To win the lottery, you must correctly guess the numbers for the MegaBall, the WinnerBalls (order does not matter), and the SpecialBall. What is the probability that the ticket I hold has the winning numbers?

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