
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 in a particular state now includes two drawings. For the first drawing, a MegaBall is chosen from among 30 numbered balls. For the second drawing, five WinnerBalls are picked sequentially (with no replacements) from among 50 numbered balls. To win this revised lottery, you must correctly guess the MegaBall number and also the exact sequence of the five WinnerBalls. 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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