
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 now two drawings. First, a MegaBall is selected from 30 numbered balls. Secondly, five WinnerBalls are picked from a different set of 46 numbered balls. To win this modified lottery, a player must correctly guess the number of the MegaBall and the numbers on the five WinnerBalls, disregarding the order of the WinnerBalls. What is the probability that a given lottery ticket will win?

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