
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 another state consists of two drawings. First, a StarBall is picked from among 30 numbered balls. Second, six MagicBalls are picked from among 49 numbered balls. To win the lottery, you must pick the StarBall number correctly and also pick the numbers on the six MagicBalls (but you don't need to get the order right for the MagicBalls). 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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