
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
Forty teams play a tournament in which every team plays every other team exactly once.  No ties occur, and each team has a  $50 \%$  chance of winning any game it plays.  The probability that no two teams win the same number of games is  $m/n,$  where  $m$  and  $n$  are relatively prime positive integers.  Find  $\log_2 n.$ 

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