
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
Suppose two distinct competitors of the HMMT 2021 November contest are chosen uniformly at random. Let \( p \) be the probability that they can be labelled \( A \) and \( B \) so that \( A \)'s score on the General round is strictly greater than \( B \)'s, and \( B \)'s score on the Theme round is strictly greater than \( A \)'s. Estimate \( P = \lfloor 10000p \rfloor \).

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