
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
At the end of a chess tournament, the top 6 players have a playoff. The seedings are such that #6 plays #5 first. The loser gets the 6th prize. The winner then plays #4, the loser of this game gets the 5th prize. The winner plays #3, the loser gets the 4th prize. This is followed by the winner playing #2, where the loser gets the 3rd prize. Finally, the winner confronts #1 and the loser receives the 2nd prize while the winner receives the 1st prize. Calculate the number of different ways the 6 prizes can be distributed among the players.

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