
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 two drawings. First, a PowerBall is selected from 30 numbered balls. Then, six LuckyBalls are drawn from a set of 49 balls. To win this lottery, a ticket must correctly guess the PowerBall and all six LuckyBalls (order of the LuckyBalls does not matter). What is the probability of holding the winning ticket?

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