
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
A "Rock, Paper, Scissors" tournament is being held in a single-elimination format with 16 players. The organizers have determined the matchups for the first round, and the winners of each match will play against one another in the following rounds until a champion is determined. Each player will make the same move (rock, paper, or scissors) throughout all their games, which they choose randomly before the first game. How many choices do the players have so that the tournament concludes with a winner?

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