
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
A tournament with 100 competitors, each with different skill levels, will take place. The most skilled competitor always wins against the less skilled one. Each participant plays exactly twice, with two randomly chosen opponents (once with each). A competitor who wins both matches receives a medal. Determine the minimum number of medals that can be distributed in the tournament.

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