
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 slight modification of a state lottery, there is a SharpBall drawn from 30 numbered balls and six PrizeBalls drawn from 50 numbered balls, in different draws. To strike the jackpot, one must correctly pick the SharpBall and the numbers on all six PrizeBalls (order of PrizeBalls does not matter). What is the probability that a ticket will have the winning numbers?

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