
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 now consists of two drawings. First, a PowerBall is picked from among 30 numbered balls. Second, six LuckyBalls are picked from among 49 numbered balls. To win the lottery, you must pick the PowerBall number correctly and also correctly pick the numbers on all six LuckyBalls (order does not matter for the LuckyBalls). 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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