
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 extended professional bowling tournament, the top 6 bowlers enter into a playoff. Initial game starts with #6 bowling against #5. The loser takes 6th place and the winner goes on to bowl against #4. The subsequent losers will take 5th, 4th, and 3rd places consecutively, as they lose against the sequential winners from previous matches respectively (#3, then #2). Finally, the remaining two bowlers compete, where the loser gets 2nd prize and the winner gets 1st prize. Determine how many orders can bowlers #1 through #6 receive the prizes.

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