
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
Ava and Tiffany participate in a knockout tournament consisting of a total of  $32$  players. In each of  $5$  rounds, the remaining players are paired uniformly at random. In each pair, both players are equally likely to win, and the loser is knocked out of the tournament. The probability that Ava and Tiffany play each other during the tournament is  $\tfrac{a}{b},$  where  $a$  and  $b$  are relatively prime positive integers. Compute  $100a + b.$ 

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