
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 new state lottery system, there are two drawings. First, a MegaBall is selected from 30 different numbered balls. Second, six WinnerBalls are chosen from a set of 50 numbered balls. To secure a lottery win, a participant must correctly guess the number of the MegaBall and the numbers of all six WinnerBalls (the order of WinnerBalls does not matter). What is the probability that a given ticket will have the winning combination?

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