
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 modified bowling tournament, the playoffs are adjusted as follows: First, bowler #3 bowls against #4. The loser of this game bowls against #5, giving them a second chance. The winner of the first game bowls against #2, and the winner of the loser's match continues competing. The contests continue until there's a match between the final winner and #1. All-round losers gain the next lowest prize not yet allocated, except the loser of the first game who has a second chance against #5. Determine the total number of different ways the prizes can be distributed.

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