
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
Westlake University is competing against Eastgate University in a chess tournament. Each university has three players, and each player must play two games against each of the other university's players. The tournament takes place over six rounds, with three games played in parallel in each round. Additionally, no repeat of a game from one round is allowed in the next round (i.e., if players A and X play in Round 1, they cannot play against each other again in Round 2). In how many different ways can the tournament be scheduled?
A) 540
B) 720
C) 900
D) 1200
E) 1296

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