
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 larger regional bowling competition, the top 6 bowlers enter the playoff matches. Initially, bowler #6 competes against bowler #5. The winner of this match plays against bowler #4, and this process continues with each subsequent winner facing the next higher-ranked bowler. The loser of each game receives the next lowest prize, starting with the 6th prize for the loser of the first game. This sequence continues until the winner of the final match receives the 1st prize, and the loser gets the 2nd prize. In how many different sequences can the prizes be distributed among bowlers #1 through #6?

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