
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 Wrestling Federation assigned each participant in the competition a qualification number. It is known that in matches between wrestlers whose qualification numbers differ by more than 2, the wrestler with the smaller number always wins. The tournament for 256 wrestlers is conducted using an Olympic system: at the beginning of each day, the fighters are paired, and the loser is eliminated from the competition (there are no ties). What is the highest qualification number that the winner can have?

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