
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 among 2021 ranked teams is played over 2020 rounds. In each round, two teams are selected uniformly at random among all remaining teams to play against each other. The better-ranked team always wins, and the worse-ranked team is eliminated. Let \( p \) be the probability that the second-best ranked team is eliminated in the last round. Compute \( \lfloor 2021 p \rfloor \).

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