
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 the lottery "6 out of 45", a participant places a bet by choosing any 6 numbers out of 45 (the order of choosing the numbers does not matter, but all numbers must be different). During the draw, a random winning combination of 6 numbers is determined. A "jackpot" is an event in which a participant's bet correctly matches all 6 winning numbers.

A player bought 100 tickets and on each selected 6 numbers such that there are no repeating combinations between any two different tickets. Estimate the probability p of hitting the "jackpot".

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