
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
Thirty teams are participating in a knockout tournament where each match results in a win or lose outcome only, and the losing team is eliminated. Each team has a $50 \%$ chance of winning any game it plays. The probability that the final sequence of winners is in the exact increasing order of their initial arbitrary labels (team 1 to team 30) is $\frac{m}{n}$, 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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