
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 have a playoff. First, #6 bowls #5. The loser receives the $6^\text{th}$ prize and the winner bowls #4. The loser of this game receives the $5^\text{th}$ prize, and the winner faces #3. The loser of this subsequent game gets the $4^\text{th}$ prize, and the winner bowls #2. The loser of this game gets the $3^\text{rd}$ prize, leaving the winner to bowl against #1. Finally, the winner of this last game gets the $1^\text{st}$ prize and the loser takes the $2^\text{nd}$ prize. In how many orders can bowlers #1 through #6 receive the prizes?

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