
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 Sports Wrestling Federation has assigned a qualification number to each participant in the competition. It is known that in matches where the qualification numbers of wrestlers differ by more than 2, the wrestler with the smaller number always wins. The tournament for 512 wrestlers is conducted in an Olympic system: at the beginning of each day, wrestlers are paired off, and the loser is eliminated from the competition (there are no draws). What is the highest qualification number that the winner can have?

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