
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 weekend softball tournament, there are six teams: A, B, C, D, E, and F. On Saturday, Team A plays Team B, Team C plays Team D, and Team E plays Team F. On Sunday, winners from these three matches play in a round-robin format to determine the top rankings (1st to 3rd places) and the losers play in another round-robin to determine the lower rankings (4th to 6th places). Teams ranked based on their wins; in case of tied wins, a stochastic decision (e.g., a coin flip) makes the final decision. What is 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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