
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
In a bowling tournament, 6 bowlers are competing for the top prizes with a playoff system. First, #6 bowls against #5, and the winner enters the main playoff with bowlers #1 through #4. The winner of #6 vs. #5 then bowls #4, the winner of which bowls #3, and so on, until they finally bowl #1. The matches continue in a knockout format where the loser of each match receives the next available lowest prize starting from 5th prize down to 2nd, after all matches. How many different orders can the bowlers receive the prizes?

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