
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 Federation of Sports Wrestling has assigned a qualification number to each participant in the competition. It is known that in matches between wrestlers whose qualification numbers differ by more than 2, the wrestler with the smaller number always wins. A tournament for 256 wrestlers is conducted in an Olympic system: at the beginning of each day, the wrestlers are divided into pairs, 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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