
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 weekend volleyball tournament, there are six teams: A, B, C, D, E, and F. On Saturday, Team A plays Team E, Team B plays Team C, and Team D plays Team F. Then on Sunday, the three Saturday winners play round-robin matches (each team plays every other team once) for first, second, and third places, while the three losers play for fourth, fifth, and sixth places. There are no ties in any game. Given that a possible ranking of the teams from first to sixth place at the end of the tournament is AECBDF, determine the total number of possible six-team ranking sequences at the end of the tournament.

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