
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 game in our town features two draws. Firstly, a MegaBall is chosen from 30 uniquely numbered balls. Secondly, six WinnerBalls are chosen from a set of 45 differently numbered balls. To win this lottery, one must correctly guess the MegaBall number and also correctly guess the numbers of the six WinnerBalls regardless of the order they are drawn in. What is the probability that the ticket I hold matches all the winning numbers?

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