
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
Miklós offers the following bet to Laci: "I will pay you 1 Ft after every lottery draw in 1967 in which the 5 drawn lottery numbers do not include 3 consecutive numbers, if you pay me 100 Ft after every draw that includes at least 3 consecutive numbers." - We learned that Miklós bases his hopes of winning on the fact that such a draw (where there are at least 3 consecutive numbers) has not occurred in the first 500 draws of the ongoing Hungarian lottery game. - On average, out of how many draws can a draw that is favorable to Miklós be expected?

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