
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
Crestwood Elementary School has expanded its four-square league to include twelve players, with Justin and Tim included among them. Each day at recess, the players split into two simultaneous games, each with six players. The team arrangements are made so that each possible combination of six players occurs exactly once throughout the semester. How many times did Justin and Tim play in the same game?

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