
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 an expanded professional bowling tournament, the top 6 bowlers proceed to the playoffs. Initially, #6 bowls against #5. The loser receives the 6th prize, and the winner faces #4. The loser of this match receives the 5th prize, and the winner proceeds to bowl against #3. The subsequent loser gets the 4th prize, and the winner bowls #2. The loser of this match takes the 3rd prize, while the winner goes on to compete against #1. Finally, the ultimate winner is awarded the 1st prize, and the loser of this final game receives the 2nd prize. In how many different orders can bowlers #1 through #6 receive the prizes?

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