
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
On the first day of a regional chess tournament, Player A competes against Player B, and Player C competes against Player D. The winners of these matches play against each other on the second day for the first and second positions, while the losers play an additional match to determine who will proceed to the third-place match. The loser of this additional match directly secures the fourth place, and the winner plays against the loser of the winners' match for the third place. Assume there are no ties in any match. What is the total number of possible four-player ranking sequences at the end of the tournament?

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